Vectors

Key Questions

• How can vectors be represented?

  A vector #vecv# can be represented as a pointed arrow drawn in space:

  

  The length of the arrow (relative to some kind of reference or scale) represents the relative magnitude of the vector while the arrow head gives us the direction in which the vector operates.

  Another way to represent a vector is by giving its components .
  Basically, in space, you choose three unit vectors ( of magnitude #1# and directions the positive ones of the #x,y and z# axes) indicated as #veci, vecj and veck# and then you do a linear combination of these three unit vectors using three components (=numbers such as #5,4 and 6#).

  

  For example, #vecu=5veci+4vecj+6veck#

  

  Basically you can think of it as a recipe of a cake where #veci, vecj and veck# are the ingredients:
  To "make" vector #vecu# you need to mix (=combine linearly):
  5 units of ingredient #veci#;
  4 units of ingredient #vecj#;
  6 units of ingredient #veck#.

  Gió · 3 · Mar 2 2015

• How do you write the components of vectors?
• How can vectors be represented?
• What does the i and j stand for in vectors?
• If #\vec{g}# is in standard position with terminal point (5, 5) and #\vec{h}# is in standard position with terminal point (4, 2), how do you find the direction of the resultant vector?
• If #\vec{i}# is in standard position with terminal point (1, 5) and #\vec{j}# is in standard position with terminal point (-3, 1), what is the coordinate of the terminal point of the resultant vector?
• How do you find the coordinates of vector PQ in standard position given Points P( 4,5) and Q (-7,3)?
• Using (-3, -2) as the initial point, how do you draw the vector that represents the complex number #2 - 9i#?
• Using (-3, -2) as the initial point, how do you draw the vector that represents the complex number #8#?
• How do you give the complex number form of the vector with the given initial and terminal point respectively (4,7) and (-3, 1)?
• How do you give the complex number form of the vector with the given initial and terminal point respectively (-2, 5) and (1, 3)?
• What is the angle between #<6,9,1># and #<5,6,7> #?
• What is the angle between #<5,7,1># and #<5,1,7> #?
• What is the angle between #<9,7,1># and #<8,3,6> #?
• What is the angle between #<4,7,1 ># and #<9,5,4> #?
• What is the angle between #<4,7,1 ># and #<9,5,4> #?
• What is the angle between #<6,8,1 ># and #< 4, 7, 3 >#?
• What is the angle between #<1,5,7 ># and #< 4, 7, 3 >#?
• What is the angle between #<1,5,7 ># and #< 6,8,1 >#?
• What is the angle between #<2,5,4 ># and #< 6,8,1 >#?
• What is the angle between #<5,1,4 ># and #< 3,1,9 >#?
• What is the angle between #<8,5,9 ># and #< 4,3,8 >#?
• What is the angle between #<1,3,9 ># and #< 4,9,2 >#?
• What is the angle between #<5,8,2 ># and #< 2,1,4 >#?
• What is the angle between #<5,8,2 ># and #< 4,6,-1 >#?
• What is the angle between #<2,7,-1 ># and #< 3,2,-8 >#?
• What is the angle between #<2,-3,-1 ># and #< -8,3,-5>#?
• What is the angle between #<1 ,3,-8># and #< 4,1,5>#?
• What is the angle between #<7,-2,8># and #< 7,3,-8>#?
• What is the angle between #<-8,2,8># and #< 2,-3,5>#?
• What is the angle between #<-8,2,8># and #< 6,-4,5>#?
• What is the angle between #<-2,5,-7 > # and #< 6,-4,5>#?
• What is the angle between #<5,9,-2 > # and #< 6,-2,7>#?
• What is the angle between #<7,-3,1 > # and #< -2,8,-5 >#?
• What is the angle between #<9,-5,1 > # and #< -7,4,2 >#?
• What is the angle between #<9,-8,1 > # and #< 4,-7,1 >#?
• What is the angle between #<-3,9,-7 > # and #< 4,-2,8 >#?
• What is the angle between #<-7,4,-7 > # and #< 4,3,0 >#?
• What is the angle between #<-7,2,-3 > # and #< 1,-5,1 >#?
• What is the angle between #<5,4,3 > # and #< 1,-5,-7 >#?
• What is the angle between #<-1,9,3 > # and #< 5,-8,2 >#?
• What is the angle between #<6,-4,-9> # and #< 5,0,2 >#?
• What is the angle between #<-3,2,0> # and #< 5,0,2 >#?
• What is the angle between #<-4,8,0> # and #< 1,0,-2>#?
• What is the angle between #<-4,8,0> # and #< -3,6,-2>#?
• What is the angle between #<7,2,-4 > # and #< -3,6,-2>#?
• What is the angle between #<-3,5,0 > # and #< 4,0,-2>#?
• What is the angle between #<-7,0 ,4> # and #< -1,5,0>#?
• What is the angle between #<0,5,4> # and #<5,-8,7>#?
• What is the angle between #<9,1,4> # and #<6,-1,4 >#?
• What is the angle between #<-2,7,-1> # and #<6,-1,4 >#?
• What is the angle between #<-9,4,0> # and #<-8,2,-7 >#?
• What is the angle between #<2,9,-2> # and #<0,3?0 >#?
• What is the angle between #<2,9,-2> # and #<0,3,0 >#?
• What is the angle between #<8,-1,2> # and #<-4,-1,3>#?
• What is the angle between #<-7,-9,-2># and #< 2,-3,5>#?
• What is the angle between #<-4,3,-8 ># and #< 1,-1,5>#?
• What is the angle between #<-4,3,-8 ># and #< 6,-3,8 >#?
• What is the angle between #<-4,0,-2 ># and #< -2,-1,4 >#?
• What is the angle between #<-1,0,6 ># and #< 2,-1,5 >#?
• What is the angle between #<-1,8,6 ># and #< -6,3,0>#?
• What is the angle between #<-1,8,2 ># and #< 0,-3,1>#?
• What is the angle between #<4,8,2 ># and #< 0,-7,1>#?
• What is the angle between #<6,9,-2># and #< -2,0,4 >#?
• What is the angle between #<-4,9,4> # and #< -2,0,4 >#?
• What is the angle between #<0,2,-8> # and #< -2,1,4 >#?
• What is the angle between #<-2,3,1> # and #< 4,1,4 >#?
• What is the angle between #<7,-3,1> # and #< -1,3,2 >#?
• What is the angle between #<-2,-5,6> # and #< -1,-1,2 >#?
• What is the angle between #<-8,0,6> # and #<3,2,-3 >#?
• What is the angle between #<-3,5,6> # and #<9,-1,8>#?
• What is the angle between #<-3,5,6> # and #<-1,9,-3>#?
• What is the angle between #<0,-7,6> # and #<-1,9,-3>#?
• What is the angle between #<0,-7,6> # and #<-1,6,-6>#?
• What is the angle between #<8,7,6> # and #<-1,6,1>#?
• What is the angle between #<<-7,5,-9>> # and #<<-1,-2,1>>#?
• What is the angle between #<-2,4,-3> # and #<-1,0,1>#?
• What is the angle between #<-8,-5,2 > # and #<9,1,-3> #?
• What is the angle between #<-1,8,8 > # and #<-1,7,3> #?
• What is the angle between #<-1,-2,8 > # and #<-2,6,-4> #?
• What is the angle between #<-1,-7,2 > # and #<-3,-5,1> #?
• What is the angle between #<-3,2,6 > # and #<5,0,-5> #?
• What is the angle between #<-3,2,6 > # and #<6,1,-5> #?
• What is the angle between #<-3,2,0 > # and #<6,-9,8> #?
• What is the angle between #<-5,-3,6 > # and #<3,9,-9> #?
• What is the angle between #<-5,7,6 > # and #<0,-4,8> #?
• What is the angle between #<-2,1,1 > # and #<1,3,8> #?
• What is the angle between #<0,9,-6 > # and #<1,3,5> #?
• What is the angle between #<6,3,-6 > # and #<1,7,-3> #?
• What is the angle between #<5,0,-2 > # and #<-8,3,-6> #?
• What is the angle between #<-4,2,-1 > # and #<-8,0,0> #?
• What is the angle between #<-4,0,1 > # and #<-6,-1,0> #?
• What is the angle between #<-4,-1,1 > # and #<-6,-1,-4> #?
• What is the angle between #<4,-2,9> # and # < 5,1,-8 > #?
• What is the angle between #<6,-2,9> # and # < -2,1,-8 > #?
• What is the angle between #<6,-2,2 > # and # < -2, 7 ,-2 > #?
• What is the angle between #<6, 8 ,2 > # and # < -2, 7 ,-2 > #?
• What is the angle between #<-3 , 5 ,2 > # and # < -2, 7 ,-2 > #?
• What is the angle between #<-3 , -5 ,1 > # and # < -4, 7 ,-2 > #?
• What is the angle between #<1 , -5 ,1 > # and # < -4, 9 , 4 > #?
• What is the angle between #<1 , 5 , 3 > # and # < 4, 9 , 4 > #?
• What is the angle between #<5 , 5 , 3 > # and # < 4, 9 , 1 > #?
• What is the angle between #<5 , 5 , -1 > # and # < 4, -3 , 1 > #?
• What is the angle between #<5 , 2 , -1 > # and # < 1, -3 , 1 > #?
• What is the angle between #<3 , 2 , -1 > # and # < 1, -3 , 6 > #?
• What is the angle between #<3 , -2 , 7 > # and # < 1, -3 , 6 > #?
• What is the angle between #<3 , -2 , 7 > # and # < 5, -3 , 2 > #?
• What is the angle between #<1 , -2 , 7 > # and # < 7 , -2 , 2 > #?
• What is the angle between #<1 , 3 , -4 > # and # < 5 , -2 , 2 > #?
• What is the angle between #<7 , -2 , -4 > # and # < 5 , -2 , 1 > #?
• What is the angle between #<7 , -2 , 7 > # and # < 2 , 5 , 1 > #?
• What is the angle between #<1 , -2 , 3 > # and # < -2 , 5 , 1 > #?
• What is the angle between #<1 , 5 , 9 > # and # < -2 , 3 , 2 > #?
• What is the angle between #<6 , 5 , 7 > # and # < 3 , 3 , 2 > #?
• What is the angle between #<6 , 5 , 7 > # and # < 3 , -4 , 8 > #?
• What is the angle between #<6 , 3 , 2 > # and # < 3 , -4 , 8 > #?
• What is the angle between #<6 , 3 , 1 > # and # < 3 , -9 , 8 > #?
• What is the angle between #<7 , 3 , 1 > # and # < 8 , -9 , 8 > #?
• What is the angle between #<7 , 3 , -3 > # and # < 8 , 6 , 8 > #?
• What is the angle between #<7 , 2 , -3 > # and # < 8 , 6 , 0 > #?
• What is the angle between #<7 , 2 , 7 > # and # < 8 , -5 , 0 > #?
• What is the angle between #<-4 , 0 , 7 > # and # < 8 , -5 , 0 > #?
• What is the angle between #<-4 , 0 , -1 > # and # < 8 , 6 , 3 > #?
• What is the angle between #<4 , 7 , -1 > # and # < -3 , 6 , 3 > #?
• What is the angle between #<4 , 7 , -4 > # and # < 5 , 2 , 3 > #?
• What is the angle between #<-9 , 2 , -4 > # and # < 5 , 2 , 0 > #?
• What is the angle between #<-9 , 2 , 2 > # and # < 5 , 8 , 3 > #?
• What is the angle between #< 6 , 2 , -4 > # and # < 2 , 8 , 3 > #?
• What is the angle between #< 6 , 1 , -4 > # and # < 2 , -3 , 2 > #?
• What is the angle between #< 4 , 1 , -2 > # and # < -9 , -3 , 2 > #?
• What is the projection of #<4 , -2 , 7 ># onto #< 2 , -5 , 8 >#?
• What is the projection of #<4 , -6, 7 ># onto #< -1 , 5, 8 >#?
• What is the projection of #<4 , -6, 7 ># onto #< -1 , 9,-2 >#?
• What is the projection of #<3 ,-4, 7 ># onto #< -1 , 9,-2 >#?
• What is the projection of #<3 ,-4, 7 ># onto #< -1 , 0, -2 >#?
• What is the projection of #<-6 , -7, 1 ># onto #< -1 , 0, -2 >#?
• What is the projection of #<-7 , -7, 1 ># onto #< 4, 0, -2 >#?
• What is the projection of #<-7 , 3, -5 ># onto #< 4, 0, -2 >#?
• What is the projection of #<-7 , 3, -5 ># onto #< 4, -5, 1>#?
• What is the projection of #< 6 , -6 ,3 ># onto #< 4, -5, 1>#?
• What is the projection of #< 6 , -6 ,3 ># onto #< 4, 9, 1>#?
• What is the projection of #< -3 , 1 ,3 ># onto #< 4, 9, 1>#?
• What is the projection of #< -3 , 1 ,3 ># onto #< 8 ,5 ,-3>#?
• What is the projection of #< -3 , 1 ,3 ># onto #< 8 , 8 , -4 >#?
• What is the projection of #< 5 ,- 3, 9 ># onto #< 8 , 8 , -4 >#?
• What is the projection of #< 5 ,- 3, 9 ># onto #< 5, -2 , -4 >#?
• What is the projection of #< 5 ,- 3, 2 ># onto #< -1 , -2 , -4 >#?
• What is the projection of #< 5 ,- 3, 2 ># onto #< 3 , -6, 7 >#?
• What is the projection of #< 0 , 2, -2 ># onto #< 3 , -6, 7 >#?
• What is the projection of #< 0 , 2, -2 ># onto #< 3 , -7, 4 >#?
• What is the projection of #< 5 , -6, 0 ># onto #< 3 , -7, 4 >#?
• What is the projection of #< 5 , -6, 0 ># onto #< -1, -4 , 6 >#?
• What is the projection of #< 3 , -7, 0># onto #< -1, -4 , 6 >#?
• What is the projection of #< 2 , -6, 0># onto #< -1, -4 , 6 >#?
• What is the projection of #< 2 , -6, 0># onto #< 5, -3, 8>#?
• What is the projection of #< -3, 6, 7># onto #< 5, -3, 8>#?
• What is the projection of #< -3, 6, 7># onto #< 5, 1, -5>#?
• What is the projection of #< -3, 7, 7># onto #< -3 , 4, -5>#?
• What is the projection of #< -1, 5, 7># onto #< 7,-3, -5>#?
• What is the projection of #< -2, -5, 7># onto #< 7,2, -5>#?
• What is the projection of #< -2, 4, 7># onto #< -5, 9, -5>#?
• If #A= <-3 ,4 ,-1 ># and #B= <8 ,-4 ,2 >#, what is #A*B#?
• If #A= <-3 ,4 ,-1 ># and #B= <8 ,-4 ,2 >#, what is #A*B -||A|| ||B||#?
• If #A= <-3 ,8 ,-1 ># and #B= <0 ,-4 ,2 >#, what is #A*B -||A|| ||B||#?
• If #A= <-3 ,8 ,-1 ># and #B= <0 ,7 ,2 >#, what is #A*B -||A|| ||B||#?
• If #A= <-3 ,3 ,-1 ># and #B= <8 ,7 ,2 >#, what is #A*B -||A|| ||B||#?
• If #A= <-3 ,3 ,-1 ># and #B= <8 ,7 ,6 >#, what is #A*B -||A|| ||B||#?
• If #A= <4, 3 ,-1 ># and #B= <8 ,7 ,6 >#, what is #A*B -||A|| ||B||#?
• If #A= <4, 3 ,-1 ># and #B= <9 ,7 ,6 >#, what is #A*B -||A|| ||B||#?
• If #A= <4, 9 ,-1 ># and #B= <9 ,-1 ,6 >#, what is #A*B -||A|| ||B||#?
• If #A= <4, 9 ,-1 ># and #B= <9 ,-1 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <6 ,9 ,-1 ># and #B= <9 ,-1 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <6 ,9 ,-1 ># and #B= <-4 ,-1 ,4 >#, what is #A*B -||A|| ||B||#?
• If #A= <6 ,9 ,-1 ># and #B= <-4 ,-9 ,4 >#, what is #A*B -||A|| ||B||#?
• If #A= <6 ,-4 ,-1 ># and #B= <-4 ,-9 ,4 >#, what is #A*B -||A|| ||B||#?
• If #A= <6 ,-4 ,-1 ># and #B= <2 ,-9 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <16 ,-4 ,-1 ># and #B= <2 ,-9 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <-5 ,-4 ,-1 ># and #B= <2 ,-9 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-5 ,-4 ,-7 ># and #B= <2 ,-9 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-5 ,3 ,-7 ># and #B= <2 ,-9 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-5 ,3 ,-7 ># and #B= <2 ,2 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-5 ,3 ,-3 ># and #B= <2 ,2 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-5 ,3 ,-3 ># and #B= <2 ,2 ,-7 >#, what is #A*B -||A|| ||B||#?
• If #A= <-5 ,-1 ,-3 ># and #B= <-6 ,-4 ,-7 >#, what is #A*B -||A|| ||B||#?
• If #A= <-5 ,6 ,-3 ># and #B= <-6 ,-4 ,4 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,6 ,-3 ># and #B= <-6 ,-4 ,4 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,1 ,-3 ># and #B= <-6 ,-4 ,0 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,6 ,-3 ># and #B= <-6 ,4 ,0 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,6 ,-3 ># and #B= <-6 ,4 ,7 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,6 ,-3 ># and #B= <-6 ,2 ,7 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,6 ,-3 ># and #B= <-8 ,2 ,7 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,8 ,-4 ># and #B= <3 ,2 ,7 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,1 ,-4 ># and #B= <3 ,2 ,7 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,1 ,-4 ># and #B= <3 ,2 ,-5 >#, what is #A*B -||A|| ||B||#?
• If #A= <-1 ,1 ,-4 ># and #B= <3 ,2 ,4 >#, what is #A*B -||A|| ||B||#?
• If #A= <-1 ,6 ,-4 ># and #B= <7 ,2 ,4 >#, what is #A*B -||A|| ||B||#?
• If #A= <-1 ,6 ,-4 ># and #B= <3, -5, 3 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,6 ,-3 ># and #B= <3, -5, 3 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,6 ,-3 ># and #B= <3 ,-1 ,5 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,6 ,-3 ># and #B= <-2 ,-1 ,5 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,7 ,-4 ># and #B= <-2 ,-1 ,5 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,7 ,-4 ># and #B= <-1 ,-9, 2 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,7 ,-4 ># and #B= <-1, -4, 2 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,-3 ,-4 ># and #B= <-1, -4, 2 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,-3 ,-4 ># and #B= <-1, 3, 7 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,-3 ,9 ># and #B= <-1, 3, 7 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,-3 ,9 ># and #B= <0 , 3, 7 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,-3 ,9 ># and #B= <-2 ,5 ,7 >#, what is #A*B -||A|| ||B||#?
• If #A= <2 ,-3 ,-3 ># and #B= <-2 ,5 ,7 >#, what is #A*B -||A|| ||B||#?
• If #A= <4, 0 ,-3 ># and #B= <-2 ,5 ,7 >#, what is #A*B -||A|| ||B||#?
• If #A= <7 ,-2 ,1 ># and #B= <-2 ,5 ,7 >#, what is #A*B -||A|| ||B||#?
• If #veca = << 7,-2,1 >># and #vecb = << -2,6,7 >>#, what is #vecacdotvecb - ||veca||cdot||vecb||#?
• If #A= <7 ,-2 ,1 ># and #B= <8 ,6 ,7 >#, what is #A*B -||A|| ||B||#?
• If #A= <7 ,-5 ,1 ># and #B= <8 ,6 ,7 >#, what is #A*B -||A|| ||B||#?
• If #A= <7 ,-5 ,1 ># and #B= <28 ,6 ,7 >#, what is #A*B -||A|| ||B||#?
• If #A= <7 ,-5 ,1 ># and #B= <4 ,1 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <8 ,-5 ,1 ># and #B= <4 ,1 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <8 ,-5 ,6 ># and #B= <7 ,1 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <8 ,-5 ,6 ># and #B= <7 ,1 ,0 >#, what is #A*B -||A|| ||B||#?
• If #A= <8 ,- 2 ,9># and #B= <5 ,1 ,0 >#, what is #A*B -||A|| ||B||#?
• If #A= <8 ,- 2 ,9># and #B= <5 ,4 ,-9 >#, what is #A*B -||A|| ||B||#?
• If #A= <8 ,-5 ,9># and #B= <5 ,4 ,-9 >#, what is #A*B -||A|| ||B||#?
• If #A= <8 ,-5 ,-5 ># and #B= <5 ,4 ,-9 >#, what is #A*B -||A|| ||B||#?
• If #A= <8 ,-5 ,-3 ># and #B= <5 ,4 ,-9 >#, what is #A*B -||A|| ||B||#?
• If #A= <6 ,-5 ,3 ># and #B= <5 ,4 ,-9 >#, what is #A*B -||A|| ||B||#?
• If #A= <6 ,-5 ,3 ># and #B= <-7 ,4 ,-9 >#, what is #A*B -||A|| ||B||#?
• If #A= <-2 ,-5 ,3 ># and #B= <-7 ,4 ,-9 >#, what is #A*B -||A|| ||B||#?
• If #A= <-2 ,-5 ,4 ># and #B= <-7 ,4 ,-9 >#, what is #A*B -||A|| ||B||#?
• If #A= <-2 ,-5 ,4 ># and #B= <3 ,4 ,-8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-2 ,-5 ,8 ># and #B= <3 ,4 ,-8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-2 ,-7 ,-1 ># and #B= <3 ,4 ,-8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-2 ,4 ,3 ># and #B= <3 ,2 ,-8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-2 ,4 ,3 ># and #B= <-1 ,2 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-2 ,1 ,3 ># and #B= <-1 ,2 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-2 ,1 ,3 ># and #B= <-9 ,2 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-2 ,3 ,3 ># and #B= <-9 ,2 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-2 ,3 ,3 ># and #B= <-9 ,4 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-2 ,3 ,-4 ># and #B= <-9 ,4 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-2 ,3 ,-4 ># and #B= <-3 ,4 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-8 ,3 ,-4 ># and #B= <-3 ,4 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-8 ,3 ,-1 ># and #B= <-3 ,4 ,8 >#, what is #A*B -||A|| ||B||#?
• If #A= <-8 ,3 ,-1 ># and #B= <-3 ,4 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <8 ,3 ,-1 ># and #B= <6 ,4 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <8 ,1 ,-1 ># and #B= <-2 ,4 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <8 ,1 ,-4 ># and #B= <-2 ,4 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <3 ,1 ,-4 ># and #B= <-9 ,4 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <3 ,1 ,-4 ># and #B= <-9 ,1 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <3 ,1 ,-4 ># and #B= <4 ,-7 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <3 ,1 ,-4 ># and #B= <4 ,-2 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <3 ,1 ,-2 ># and #B= <4 ,-2 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A= <5 ,1 ,-2 ># and #B= <4 ,-2 ,3 >#, what is #A*B -||A|| ||B||#?
• If #A = <2 ,4 ,-1 >#, #B = <-1 ,8 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,4 ,-9 >#, #B = <-1 ,8 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,4 ,-9 >#, #B = <3 ,0 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,4 ,-9 >#, #B = <3 ,1 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,4 ,-3 >#, #B = <3 ,1 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,4 ,-3 >#, #B = <3 ,4 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,4 ,-3 >#, #B = <3 ,4 ,1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,1 ,-3 >#, #B = <3 ,4 ,1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <-7 ,1 ,-3 >#, #B = <3 ,4 ,1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <-7 ,1 ,-3 >#, #B = <3 ,6 ,1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <-7 ,1 ,5 >#, #B = <3 ,6 ,1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <-7 ,1 ,5 >#, #B = <3 ,6 ,-2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,1 ,5 >#, #B = <3 ,6 ,-2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,1 ,5 >#, #B = <4 ,6 ,-2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,1 ,5 >#, #B = <4 ,6 ,-1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <36 ,1 ,5 >#, #B = <4 ,6 ,-1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,1 ,-1 >#, #B = <4 ,6 ,-1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,1 ,-1 >#, #B = <4 ,-7 ,-1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,8 ,-1 >#, #B = <4 ,-7 ,-1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,8 ,-1 >#, #B = <4 ,-3 ,-1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,8 ,8 >#, #B = <4 ,-3 ,-1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,-1 ,8 >#, #B = <4 ,-3 ,-1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,-1 ,8 >#, #B = <4 ,-3 ,-6 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,-1 ,8 >#, #B = <2 ,-3 ,5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,-1 ,3 >#, #B = <2 ,-3 ,5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,-1 ,3 >#, #B = <2 ,-2 ,5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,-1 ,3 >#, #B = <2 ,-2 ,5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,-1 ,3 >#, #B = <2 ,-7 ,5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,4 ,3 >#, #B = <2 ,-7 ,5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,4 ,3 >#, #B = <2 ,-7 ,6 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,4 ,8 >#, #B = <2 ,-7 ,6 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,2 ,8 >#, #B = <2 ,7 ,6 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,2 ,8 >#, #B = <2 ,5 ,6 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,2 ,8 >#, #B = <2 ,5 ,3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,2 ,8 >#, #B = <6 ,5 ,3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,2 ,5 >#, #B = <6 ,5 ,3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,2 ,-5 >#, #B = <6 ,5 ,3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,2 ,-5 >#, #B = <6 ,5 ,9 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,2 ,-5 >#, #B = <6 ,5 ,9 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,2 ,-5 >#, #B = <6 ,4 ,9 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,2 ,-5 >#, #B = <-8 ,4 ,9 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,2 ,1 >#, #B = <-8 ,4 ,9 ># and #C=A-B#, what is the angle between A and C?
• If #A = <-5 ,2 ,1 >#, #B = <-8 ,4 ,9 ># and #C=A-B#, what is the angle between A and C?
• If #A = <-5 ,2 ,1 >#, #B = <-8 ,4 ,2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <-5 ,2 ,1 >#, #B = <-8 ,7 ,2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <-6 ,2 ,1 >#, #B = <-8 ,7 ,2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <-6 ,2 ,1 >#, #B = <-8 ,8 ,4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <-6 ,2 ,1 >#, #B = <-8 ,3 ,4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <-6 ,2 ,5 >#, #B = <-8 ,3 ,4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <-9 ,2 ,5 >#, #B = <-8 ,3 ,4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <-9 ,2 ,5 >#, #B = <-8 ,3 ,6 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,2 ,5 >#, #B = <-8 ,3 ,6 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,2 ,5 >#, #B = <-8 ,2 ,8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,2 ,5 >#, #B = <6 ,2 ,8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,2 ,5 >#, #B = <6 ,2 ,-7 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,2 ,5 >#, #B = <6 ,2 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,1 ,5 >#, #B = <6 ,2 ,-2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,1 ,5 >#, #B = <6 ,7 ,-2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,1 ,8 >#, #B = <6 ,7 ,-2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,1 ,8 >#, #B = <6 ,7 ,3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,1 ,8 >#, #B = <5 ,7 ,3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,1 ,8 >#, #B = <5 ,7 ,3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,1 ,8 >#, #B = <5 ,2 ,3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,1 ,6 >#, #B = <5 ,2 ,3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,1 ,6 >#, #B = <5 ,1 ,3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,1 ,6 >#, #B = <5 ,1 ,7 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,3 ,6 >#, #B = <5 ,1 ,7 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,3 ,-4 >#, #B = <5 ,1 ,4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,3 ,-4 >#, #B = <5 ,1 ,2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,3 ,-4 >#, #B = <6 ,1 ,2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,3 ,-1 >#, #B = <6 ,1 ,2 ># and #C=A-B#, what is the angle between A and C?
• If #veca = << 2,4,-1 >>#, #vecb = << 6,1,2 >># and #vecc = veca - vecb#, what is the angle between #veca# and #vecc#?
• If #A = <2 ,4 ,-1 >#, #B = <3 ,8 ,2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,4 ,-7 >#, #B = <3 ,8 ,2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,4 ,-7 >#, #B = <3 ,5 ,2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,4 ,-7 >#, #B = <3 ,5 ,2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,4 ,-7 >#, #B = <3 ,5 ,0 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,4 ,-7 >#, #B = <3 ,-1 ,0 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,4 ,9 >#, #B = <3 ,-1 ,0 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,4 ,9 >#, #B = <7 ,-1 ,5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,4 ,-3 >#, #B = <7 ,-1 ,5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,4 ,-3 >#, #B = <7 ,1 ,-4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,8 ,-3 >#, #B = <7 ,1 ,-4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,8 ,2 >#, #B = <7 ,1 ,-4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,7 ,2 >#, #B = <7 ,1 ,-4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,7 ,2 >#, #B = <1 ,1 ,-4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,-9 ,2 >#, #B = <1 ,1 ,-4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,-9 ,2 >#, #B = <1 ,-3 ,-8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,-9 ,5 >#, #B = <1 ,-3 ,-8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,-7 ,5 >#, #B = <1 ,-3 ,-8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,-7 ,5 >#, #B = <1 ,-5 ,-8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,-7 ,8 >#, #B = <1 ,-5 ,-8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,-7 ,8 >#, #B = <1 ,-5 ,-2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,-7 ,8 >#, #B = <9 ,-5 ,-2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,6 ,-3 >#, #B = <-9 ,7 ,-2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <6 ,6 ,-3 >#, #B = <-9 ,6 ,-2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,6 ,-3 >#, #B = <-9 ,6 ,-2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,6 ,-3 >#, #B = <-9 ,6 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,6 ,6 >#, #B = <-9 ,6 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <5 ,6 ,9 >#, #B = <-9 ,-6 ,7 ># and #C=A-B#, what is the angle between A and C?
• If #A = <1 ,6 ,9 >#, #B = <-9 ,-6 ,7 ># and #C=A-B#, what is the angle between A and C?
• If #A = <1 ,6 ,9 >#, #B = <-9 ,-6 ,-8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <1 ,6 ,9 >#, #B = <-9 ,4 ,-8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <1 ,6 ,-8 >#, #B = <-9 ,4 ,-8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <1 ,6 ,-8 >#, #B = <-9 ,4 ,0 ># and #C=A-B#, what is the angle between A and C?
• If #A = <1 ,6 ,-8 >#, #B = <-9 ,4 ,1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,6 ,-8 >#, #B = <-9 ,4 ,1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,6 ,-8 >#, #B = <-9 ,4 ,-2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,-5 ,-8 >#, #B = <-9 ,4 ,-2 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,-5 ,-8 >#, #B = <-9 ,4 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,-5 ,9 >#, #B = <-9 ,4 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,-5 ,9 >#, #B = <-9 ,1 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,-5 ,-4 >#, #B = <-9 ,1 ,9 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,-5 ,-4 >#, #B = <-9 ,1 ,7 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,-5 ,-4 >#, #B = <-9 ,1 ,-6 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,-5 ,-4 >#, #B = <-9 ,1 ,-6 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,-5 ,-4 >#, #B = <5 ,1 ,-6 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,-5 ,-4 >#, #B = <5 ,1 ,-3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,-5 ,1 >#, #B = <5 ,1 ,-3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,-5 ,1 >#, #B = <5 ,8 ,-3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,9 ,1 >#, #B = <5 ,8 ,-3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,9 ,-7 >#, #B = <5 ,8 ,-3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,3 ,-7 >#, #B = <5 ,8 ,-3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,3 ,-7 >#, #B = <5 ,7 ,-3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,3 ,-7 >#, #B = <5 ,7 ,-4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <4 ,3 ,-7 >#, #B = <5 ,8 ,-4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,3 ,-7 >#, #B = <5 ,8 ,-4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,-1 ,-7 >#, #B = <5 ,8 ,-4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,-1 ,-7 >#, #B = <5 ,6 ,-4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,-1 ,-8 >#, #B = <5 ,6 ,-9 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,-1 ,5 >#, #B = <5 ,2 ,-9 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,-1 ,5 >#, #B = <5 ,2 ,8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,2 ,5 >#, #B = <5 ,2 ,8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,2 ,5 >#, #B = <5 ,4 ,8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <3 ,2 ,5 >#, #B = <5 ,-7 ,8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,2 ,5 >#, #B = <5 ,-7 ,8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,2 ,5 >#, #B = <5 ,-7 ,-1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,-7 ,5 >#, #B = <5 ,-7 ,-1 ># and #C=A-B#, what is the angle between A and C?
• If #A = {2,-7 ,5}#, #B = {5,-7,4}# and #C = A - B#, what is the angle between A and C?
• If #A = <2 ,-8 ,5 >#, #B = <5 ,-7 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <2 ,-8 ,5 >#, #B = <4 ,-7 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <7 ,-3 ,5 >#, #B = <4 ,-7 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <7 ,-3 ,6 >#, #B = <4 ,-7 ,-5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <7 ,-5 ,6 >#, #B = <4 ,4 ,9 ># and #C=A-B#, what is the angle between A and C?
• If #A = <7 ,-5 ,6 >#, #B = <4 ,-8 ,9 ># and #C=A-B#, what is the angle between A and C?
• If #A = <7 ,-5 ,-2 >#, #B = <4 ,-8 ,9 ># and #C=A-B#, what is the angle between A and C?
• If #A = <7 ,-8 ,-2 >#, #B = <4 ,-8 ,9 ># and #C=A-B#, what is the angle between A and C?
• If #A = <7 ,-8 ,-2 >#, #B = <4 ,-8 ,8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <7 ,-8 ,-2 >#, #B = <4 ,-8 ,5 ># and #C=A-B#, what is the angle between A and C?
• If #A = <7 ,-5 ,-2 >#, #B = <4 ,-8 ,-3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <7 ,-5 ,4 >#, #B = <4 ,-8 ,-3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <7 ,-5 ,4 >#, #B = <4 ,7 ,-3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <7 ,9 ,4 >#, #B = <4 ,6 ,-3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <7 ,9 ,4 >#, #B = <6 ,-9 ,-3 ># and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,9 ,4 >#, #B = <6 ,-9 ,-1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,9 ,4 >#, #B = <6 ,7 ,-1 ># and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,9 ,4 >#, #B = <6 ,7 ,4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,0 ,4 >#, #B = <6 ,7 ,4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,0 ,4 >#, #B = <6 ,5 ,4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,1 ,4 >#, #B = <6 ,5 ,4 ># and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,1 ,4 >#, #B = <6 ,5 ,-8 ># and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,1 ,-5 >#, #B = <6 ,5 ,-8 ># and #C=A-B#, what is the angle between A and C?
• If #veca = <8 ,1 ,-5 >#, #vecb = <6 ,-2 ,-8 ># and #vecc=veca-vecb#, what is the angle between #veca# and #vecc#?
• If #A = <8 ,1 ,-5 >#, #B = <6 ,-2 ,4 >#, and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,1 ,-7 >#, #B = <6 ,-2 ,5 >#, and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,3 ,-7 >#, #B = <6 ,-9 ,5 >#, and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,3 ,-7 >#, #B = <6 ,-4 ,5 >#, and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,3 ,2 >#, #B = <6 ,-4 ,5 >#, and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,3 ,2 >#, #B = <6 ,-1 ,5 >#, and #C=A-B#, what is the angle between A and C?
• If #A = <8 ,3 ,2 >#, #B = <-1 ,-1 ,5 >#, and #C=A-B#, what is the angle between A and C?
• Raindrops are falling vertically at a speed of 120 km/h through air that is moving horizontally at a speed of 40 km/h(i.e. the wind is 40 km/h). At what angle do the drops strike the ground?
• Raindrops are falling vertically at a speed of 120 km/h through air that is moving horizontally at a speed of 40 km/h(i.e. the wind is 40 km/h). How fast are the drops actually going?
• An airplane flies on a course of 110° at a speed of 1200 km/h. How far east of its starting point is it after 2 h?
• If#" "veca=3hati+4hatj+5hatk and vec b= 2hati+hatj-4hatk# ;How will you find out the component of #" "veca " ""perpendicular to" " " vecb#?
• Two non collinear position vectors #veca & vecb# are inclined at an angle #(2pi)/3#,where #|veca|=3 & |vecb|=4 #. A point P moves so that #vec(OP)=(e^t+e^-t)veca +(e^t-e^-t)vecb#. The least distance of P from origin O is #sqrt2sqrt(sqrtp-q)# then p+q =?
• Two non collinear position vectors #veca & vecb# are inclined at an angle #(2pi)/3#,where #|veca|=3 & |vecb|=4 #. A point P moves so that #vec(OP)=(e^t+e^-t)veca +(e^t-e^-t)vecb#. The least distance of P from origin O is #sqrt2sqrt(sqrtp-q)# then p+q =?
• Question #d2701
• Question #64850
• How do you find the inner product #<3,-2,4>*<1,-4,0>#?
• How do you find the cross product of #<2,3,0># and #2<-1,2,4>#?
• How do you find the component form and magnitude of the vector v given initial point (-1,5) and terminal point (15, 12)?
• How do you find the component form and magnitude of the vector v given initial point (1,11) and terminal point (9,3)?
• How do you find the component form and magnitude of the vector v given initial point (-3,-5) and terminal point (5,1)?
• How do you find the component form and magnitude of the vector v given initial point (-3,11) and terminal point (9,40)?
• How do you find the component form and magnitude of the vector v given initial point (1,3) and terminal point (-8,-9)?
• How do you find the component form and magnitude of the vector v given initial point (-2,7) and terminal point (5,-17)?
• How do you find a) u+v, b) u-v, c) 2u-3v given #u=<2,3>, v=<4,0>#?
• How do you find a) u+v, b) u-v, c) 2u-3v given #u=<-5,3>, v=<0,0>#?
• How do you find a) u+v, b) u-v, c) 2u-3v given #u=<0,0>, v=<2,1>#?
• How do you find a) u+v, b) u-v, c) 2u-3v given #u=i+j, v=2i-3j#?
• How do you find a) u+v, b) u-v, c) 2u-3v given #u=-2i+j, v=-i+2j#?
• How do you find a) u+v, b) u-v, c) 2u-3v given #u=2i, v=j#?
• How do you find a) u+v, b) u-v, c) 2u-3v given #u=3j, v=2i#?
• Question #d62c9
• Question #46110
• Finding coordinates of points using vectors? (See picture)
• A helicopter at A(6, 9, 3) moves with constant velocity. 10 minutes later, it is at B(3, 10, 2.5) Distances are in kilometres. At what angle to the horizontal does is the helicopter flying?
• Boat A's position is given by #x_a(t)=3-t, y_a(t)=2t-4# and boat B's position is given by #x_b(t)=4-3t, y_b(t)=3-2t#. The distance units are kilometres and the time units are hours. At what time are the boats closest to each other?
• Find a dot b given that ...(please see description)? Thanks
• Question #420ec
• If #a# and #b# are unit vectors and #theta# is the angle between them, express #abs(a-b)# in terms of #theta# ?
• Question #2ad9d