# Vector Operations

### Topic Page

Vector Operations### Questions

- What are vectors used for?
- Why vectors cannot be added algebraically?
- How do we represent the magnitude of a vector in physics?
- How do you find the equation of a vector orthogonal to a plane?
- Why are vectors important?
- How does a vector quantity differ from a scalar quantity?
- How can I calculate the magnitude of vectors?
- How do vectors subtract graphically?
- How do force vectors affect an object in motion?
- How can vectors be represented?
- How can vectors be combined?
- What are some examples of vectors?
- What are vectors?
- Question #5de41
- Question #8f0b0
- The two vectors A and B in the figure have equal magnitudes of 13.5 m and the angles are θ1 = 33° and θ2 = 110°. How to find (a) the x component and (b) the y component of their vector sum R , (c) the magnitude of R, and (d) the angle R ?
- What is the dot product of two vectors?
- Question #8599d
- Question #8bef5
- The wind exerts a force of 452 N north on a sailboat, while the water exerts a force of 325 N west on the sailboat. What is the magnitude and direction of the net force on the sailboat?
- Question #b00d1
- What are the parallelogram and the polygon methods?
- The #x# component of a vector is 8.7 units, and its #y# component is 06.5 units. What is the magnitude?
- What is the cross product of #[5, 6, -3]# and #[5, 2, 9]#?
- What is the cross product of #[1, -2, -3]# and #[3, 7, 9]#?
- What is the cross product of #[1, 3, 4]# and #[3, 7, 9]#?
- What is the cross product of #[1, -2, -3]# and #[1, 3, 4]#?
- What is the cross product of #[2, -5, 8] # and #[3, 7, 9]#?
- What is the cross product of #[1, -2, -3]# and #[2, -5, 8] #?
- What is the cross product of #[1, 3, 4]# and #[2, -5, 8] #?
- What is the cross product of #[1, 3, 4]# and #[3,2, 5] #?
- What is the cross product of #[3,2, 5]# and #[2, -5, 8] #?
- What is the cross product of #[3,2, 5]# and #[3, 1, 0] #?
- What is the cross product of #[2, 4, 5]# and #[2, -5, 8] #?
- What is the cross product of #[3,2, 5]# and #[2, 4, 8] #?
- What is the cross product of #[3,2, 5]# and #[1,2,-4] #?
- What is the cross product of #[3,2, 5]# and #[0,8,5] #?
- What is the cross product of #[0,8,5]# and #[2, 4, 8] #?
- What is the cross product of #[0,8,5]# and #[1,2,-4] #?
- What is the cross product of #[2, -1, 1]# and #[3,-6,4] #?
- What is the cross product of #[3, 0, 5]# and #[3,-6,4] #?
- What is the cross product of #[0,8,5]# and #[1, 4, -2] #?
- What is the cross product of #[1, 4, -2]# and #[3,-6,4] #?
- What is the cross product of #[1, 4, -2]# and #[2, -1, 1] #?
- What is the cross product of #[1, 4, -2]# and #[3, 0, 5] #?
- What is the cross product of #[3, 0, 5]# and #[2, -1, 1] #?
- What is the cross product of #[3, 0, 5]# and #[1,2,1] #?
- What is the cross product of #[1,2,1]# and #[2, -1, 1] #?
- What is the cross product of #[3,1,-5]# and #[2, -1, 1] #?
- What is the cross product of #[1,2,1]# and #[3,1,-5] #?
- What is the cross product of #[4,-3,2]# and #[3,1,-5] #?
- What is the cross product of #[4,-3,2]# and #[1,-2,3] #?
- What is the cross product of #[4,-3,2]# and #[-1,-1,2] #?
- What is the cross product of #[-1,-1,2]# and #[1,-2,3] #?
- What is the cross product of #[-3,0,1]# and #[1,-2,3] #?
- What is the cross product of #[-3,0,1]# and #[0,1,2] #?
- What is the cross product of #[2,4,5]# and #[0,1,2] #?
- What is the cross product of #[2,4,5]# and #[-1,0,1] #?
- What is the cross product of #[-1,0,1]# and #[0,1,2] #?
- What is the cross product of #[-1,0,1]# and #[3, 1, -1] #?
- What is the cross product of #[-3, 1, -1]# and #[0,1,2] #?
- What is the cross product of #[2,-1,2]# and #[5,1,-3] #?
- What is the cross product of #[2,-1,2]# and #[3,-1,2] #?
- What is the cross product of #[3,-1,2]# and #[5,1,-3] #?
- What is the cross product of #[2,-1,2]# and #[1,-1,3] #?
- What is the cross product of #[1,-1,3]# and #[5,1,-3] #?
- What is the cross product of #[2,-1,2]# and #[4,-3,1] #?
- What is the cross product of #[4,-3,1]# and #[1,-1,3] #?
- What is the cross product of #[3,-1,2]# and #[1,-1,3] #?
- What is the cross product of #[3,-1,2]# and #[-2,0,3] #?
- What is the cross product of #[-2,0,3]# and #[1,-1,3] #?
- What is the cross product of #[3,-1,2]# and #[1,-2,-1] #?
- What is the cross product of #[1,-2,-1]# and #[1,-1,3] #?
- What is the cross product of #[1,-2,-1]# and #[-2,0,3] #?
- What is the cross product of #[1,-2,-1]# and #[0, -1, 1] #?
- What is the cross product of #[1,-2,-1]# and #[4,3,6] #?
- What is the cross product of #[9,4,-1]# and #[4,3,6] #?
- What is the cross product of #[2, 1, -4]# and #[4,3,6] #?
- What is the cross product of #[9,4,-1]# and #[2, 1, -4] #?
- What is the cross product of #[1, -4, 0]# and #[4,3,6] #?
- What is the cross product of #<< -1, -1, 2 >># and #<< 4,3,6 >> #?
- What is the cross product of #[9,4,-1]# and #[-1, -1, 2] #?
- What is the cross product of #[-1, 2, 2]# and #[4,3,6] #?
- What is the cross product of #[3, 2, 5]# and #[4,3,6] #?
- What is the cross product of #[9,4,-1]# and #[2, 5, 4] #?
- What is the cross product of #[2, 5, 4]# and #[4,3,6] #?
- What is the cross product of #[2, 1, -4]# and #[1, -4, 0] #?
- What is the cross product of #[2, 1, -4]# and #[-1, -1, 2] #?
- What is the cross product of #[-1, -1, 2]# and #[1, -4, 0] #?
- What is the cross product of #[3, 2, 5]# and #[1, -4, 0] #?
- What is the cross product of #[2, 1, -4]# and #[3, 2, 5] #?
- What is the cross product of #[2, 5, 4]# and #[1, -4, 0] #?
- What is the cross product of #[-1, -1, 2]# and #[-1, 2, 2] #?
- What is the cross product of #[3, 2, 5]# and #[-1, 2, 2] #?
- What is the cross product of #[-1, -1, 2]# and #[3, 2, 5] #?
- What is the cross product of #[-1, -1, 2]# and #[2, 5, 4] #?
- What is the cross product of #[2, 5, 4]# and #[-1, 2, 2] #?
- What is the cross product of #[2, -1, 4]# and #[-1, 2, 2] #?
- What is the cross product of #[2, -1, 4]# and #[5, 2, -2] #?
- What is the cross product of #[4, -4, 4]# and #[5, 2, -2] #?
- What is the cross product of #[4, -4, 4]# and #[-6, 5, 1] #?
- What is the cross product of #[1, -3, 2]# and #[-8, 5, 1] #?
- What is the cross product of #[4, 0, 1]# and #[-1, 2, 3] #?
- What is the cross product of #[-1, 2, 3]# and #[-8, 5, 1] #?
- What is the cross product of #[-1, 2, 3]# and #[1, -3, 2] #?
- What is the cross product of #[-3, 5, -3]# and #[1, -3, 2] #?
- What is the cross product of #[-3, 5, -3]# and #[4, -11, 11] #?
- What is the cross product of #[3, 1, -4]# and #[1, 1, 18] #?
- What is the cross product of #[3, -4, 2]# and #[1, 1, 18] #?
- What is the cross product of #[3, 1, -4]# and #[3, -4, 2] #?
- What is the cross product of #[3, 1, -4]# and #[2, 6, -1] #?
- What is the cross product of #[2, 6, -1]# and #[1, 1, 18] #?
- What is the cross product of #[2, 6, -1]# and #[3, -4, 2] #?
- What is the unit vector that is normal to the plane containing <2i+7j-2k> and <8i-2j+3k>?
- What is the unit vector that is normal to the plane containing 3i+7j-2k and 8i+2j+9k?
- How do you normalize 3i+7j-2k?
- How do you normalize 8i+2j+9k?
- How do you normalize <0,2,0>?
- What is the unit vector that is normal to the plane containing <0,2,0> and <-1,1,1>?
- What is the unit vector that is normal to the plane containing <1,1,1> and <2,0,-1>?
- How do you normalize <2,0,-1>?
- What is the unit vector that is normal to the plane containing #(- 3 i + j -k)# and #(2i+ j - 3k)#?
- How do you normalize #(- 3 i + j -k)#?
- How do you normalize #(- 3 i + 12j -k)#?
- How do you normalize #(- 3 i + 12j -5k)#?
- How do you normalize #(- 7 i -j -25k)#?
- How do you normalize #(- 7 i -j +25k)#?
- How do you normalize #(7 i -j +2k)#?
- How do you normalize #(2 i -3j -k)#?
- What is the unit vector that is normal to the plane containing #(2i - 3 j +k )# and #(2i+ j - 3k)#?
- What is the unit vector that is normal to the plane containing #(- 3 i + j -k)# and #(2i - 3 j +k )#?
- How do you normalize #(2i - 3 j +k)#?
- What is the unit vector that is normal to the plane containing #(- 3 i + j -k)# and #(- 2i - j - k)?
- How do you normalize #(- 2i - j - k)#?
- What is the unit vector that is normal to the plane containing #(3i + 4j - k)# and #(2i+ j - 3k)#?
- What is the unit vector that is normal to the plane containing #(- 3 i + j -k)# and #(3i + 4j - k)#?
- What is the unit vector that is normal to the plane containing #(- 4i + 5 j-k)# and #(2i+ j - 3k)?
- What is the unit vector that is normal to the plane containing #(- 3 i + j -k)# and #(- 4i + 5 j - 3k)?
- How do you normalize #(- 4i + 5 j- k)#?
- How do you normalize #(i+2j+2k)#?
- What is the unit vector that is normal to the plane containing #(- 3 i + j -k)# and #(i+2j+2k)?
- What is the unit vector that is normal to the plane containing #(i+2j+2k)# and #(2i+ j - 3k)?
- What is the unit vector that is normal to the plane containing #(- 3 i + j -k)# and #( i +k )?
- What is the unit vector that is normal to the plane containing #( i +k )# and #(2i+ j - 3k)?
- What is the unit vector that is normal to the plane containing #( i +k)# and #(i+2j+2k) #?
- How do you normalize #(i+k)#?
- How do you normalize #( i - 2 j + 3 k )#?
- What is the unit vector that is normal to the plane containing # ( i +k) # and # ( i - 2 j + 3 k ) #?
- What is the unit vector that is normal to the plane containing # ( i - 2 j + 3 k ) # and # (i+2j+2k) #?
- How do you normalize #( i + 7 j + 4 k )#?
- What is the unit vector that is normal to the plane containing # ( i +k) # and # ( i + 7 j + 4 k) #?
- What is the unit vector that is normal to the plane containing # ( i - 2 j + 3 k) # and # ( i + 7 j + 4 k) #?
- How do you normalize #( - 4 i - 5 j + 2 k )#?
- What is the unit vector that is orthogonal to the plane containing # ( - 4 i - 5 j + 2 k) # and # ( i + 7 j + 4 k) #?
- What is the unit vector that is orthogonal to the plane containing # ( i - 2 j + 3 k) # and # ( - 4 i - 5 j + 2 k) #?
- What is the unit vector that is orthogonal to the plane containing # ( i - 2 j + 3 k) # and # (4 i + 4 j + 2 k) #?
- What is the unit vector that is orthogonal to the plane containing # ( i - 2 j + 3 k) # and # ( - 5 i + 4 j - 5 k) #?
- What is the unit vector that is orthogonal to the plane containing # ( - 4 i - 5 j + 2 k) # and # (4 i + 4 j + 2 k) #?
- What is the unit vector that is orthogonal to the plane containing # ( - 5 i + 4 j - 5 k) # and # (4 i + 4 j + 2 k) #?
- What is the unit vector that is orthogonal to the plane containing # ( - 4 i - 5 j + 2 k) # and # (- 5 i + 4 j - 5 k) #?
- How do you normalize #( - 4 i - 5 j + 2 k )#?
- How do you normalize #( - 5 i + 4 j - 5 k )#?
- What is the projection of #<3, -6, 2># onto #<1, 1, 1>#?
- How do you normalize #<3, -6, 2>#?
- What is the unit vector that is orthogonal to the plane containing # <3, -6, 2> # and # <1, 1, 1> #?
- What is the projection of #<< 3, -6, 2 >># onto #<< 3, 2, 1 >>#?
- How do you normalize #<3, 2, 1>#?
- What is the unit vector that is orthogonal to the plane containing # <3, -6, 2> # and # <3, 2, 1> #?
- What is the unit vector that is orthogonal to the plane containing # <3, 2, 1> # and # <1, 1, 1> #?
- How do you normalize #<0, 1, 3>#?
- What is the projection of #<3, -6, 2># onto #<0, 1, 3>#?
- What is the projection of #<0, 1, 3># onto #<3, 2, 1>#?
- What is the unit vector that is orthogonal to the plane containing # <0, 4, 4> # and # <1, 1, 1> #?
- What is the unit vector that is orthogonal to the plane containing # <0, 4, 4> # and # <1, -1, 1> #?
- How do you normalize #<0, 4, 4>#?
- What is the projection of #<0, 1, 3># onto #<0, 4, 4>#?
- What is the unit vector that is orthogonal to the plane containing # (29i-35j-17k) # and # (41j+31k) #?
- What is the unit vector that is orthogonal to the plane containing # (32i-38j-12k) # and # (41j+31k) #?
- What is the unit vector that is orthogonal to the plane containing # (29i-35j-17k) # and # (32i-38j-12k) #?
- How do you normalize # (18i -30j -12k) #?
- What is the projection of #(32i-38j-12k)# onto # (18i -30j -12k)#?
- What is the unit vector that is orthogonal to the plane containing # (20j +31k) # and # (32i-38j-12k) #?
- What is the unit vector that is orthogonal to the plane containing # (29i-35j-17k) # and # (20j +31k) #?
- What is the unit vector that is orthogonal to the plane containing # (i + j - k) # and # ( i - j + k) #?
- What is the projection of #(-i + j + k)# onto # ( i - j + k)#?
- What is the unit vector that is orthogonal to the plane containing # (-i + j + k) # and # ( i - j + k) #?
- What is the projection of #(-i + j + k)# onto # ( i - j + k)#?
- What is the projection of #(3i + 2j - 3k)# onto # ( i - j + k)#?
- What is the projection of #(-i + j + k)# onto # ( 3i + 2j - 3k)#?
- What is the unit vector that is orthogonal to the plane containing # (3i + 2j - 3k) # and # ( i - j + k) #?
- What is the unit vector that is orthogonal to the plane containing # (-i + j + k) # and # (3i + 2j - 3k) #?
- What is the projection of #(-i + j + k)# onto # ( i -2j + 3k)#?
- What is the projection of #(i -2j + 3k)# onto # ( 3i + 2j - 3k)#?
- How do you normalize # (i -2j + 3k) #?
- What is the unit vector that is orthogonal to the plane containing # (i -2j + 3k) # and # ( i - j + k) #?
- What is the unit vector that is orthogonal to the plane containing # (-i + j + k) # and # (i -2j + 3k) #?
- What is the unit vector that is orthogonal to the plane containing # (3i + 2j - 3k) # and # (i -2j + 3k) #?
- How do you normalize # (2i+j+2k) #?
- What is the projection of #(i -2j + 3k)# onto # ( 2i+j+2k)#?
- What is the unit vector that is orthogonal to the plane containing # (3i + 2j - 3k) # and # (2i+j+2k) #?
- What is the projection of #(j+2k)# onto # ( i+2j)#?
- How do you normalize # (8i + 12j + 14k) #?
- What is the unit vector that is orthogonal to the plane containing # (8i + 12j + 14k) # and # (2i+j+2k) #?
- How do you normalize # (3i – 4j + 4k) #?
- What is the projection of #(8i + 12j + 14k)# onto # (3i – 4j + 4k)#?
- What is the unit vector that is orthogonal to the plane containing # (3i – 4j + 4k) # and # (2i+j+2k) #?
- What is the unit vector that is orthogonal to the plane containing # (8i + 12j + 14k) # and # (3i – 4j + 4k) #?
- How do you normalize # (2i + 3j – 7k) #?
- What is the projection of #(8i + 12j + 14k)# onto # (2i + 3j – 7k)#?
- What is the projection of #(2i + 3j – 7k)# onto # (3i – 4j + 4k)#?
- What is the unit vector that is orthogonal to the plane containing # (8i + 12j + 14k) # and # (2i + 3j – 7k) #?
- What is the unit vector that is orthogonal to the plane containing # (2i + 3j – 7k) # and # (3i – 4j + 4k) #?
- What is the unit vector that is orthogonal to the plane containing # (3i + 2j - 6k) # and # (3i – 4j + 4k) #?
- What is the unit vector that is orthogonal to the plane containing # (2i + 3j – 7k) # and # (3i + 2j - 6k) #?
- How do you normalize # (3i + 2j - 6k) #?
- What is the projection of #(3i + 2j - 6k)# onto # (3i – 4j + 4k)#?
- How do you normalize # (3i - j - 2k) #?
- What is the projection of #(3i - j - 2k)# onto # (3i – 4j + 4k)#?
- What is the projection of #(3i + 2j - 6k)# onto # (3i - j - 2k)#?
- What is the unit vector that is orthogonal to the plane containing # (3i - j - 2k) # and # (3i – 4j + 4k) #?
- What is the unit vector that is orthogonal to the plane containing # (2i + 3j – 7k) # and # (3i - j - 2k) #?
- How do you normalize # (-2i- 3j + 2k) #?
- What is the projection of #(3i + 2j - 6k)# onto # (-2i- 3j + 2k)#?
- What is the unit vector that is orthogonal to the plane containing # (-2i- 3j + 2k) # and # (3i – 4j + 4k) #?
- What is the unit vector that is orthogonal to the plane containing # (2i + 3j – 7k) # and # (-2i- 3j + 2k) #?
- How do you normalize # (5i- 3j + 12k) #?
- How do you normalize # (15i- 3j + 12k) #?
- What is the dot product of #<5,1,-7># and #<8,4,9>#?
- What is the dot product of #<-2,5,-7># and #<8,-3,1>#?
- What is the dot product of #<7,-3, 9 ># and #<4,2,-9 >#?
- What is the dot product of #<5,-3,6 ># and #<-8,2,-9 >#?
- What is the dot product of #<3,-7,6 ># and #<4,1,7 >#?
- What is the dot product of #<3,5,-3 ># and #<-3,6,3 >#?
- What is the dot product of #<1,5,-3 ># and #<-8,3,-5 >#?
- What is the dot product of #<1,5,-3 ># and #<-1,4,2 >#?
- What is the dot product of #<1,4,-7 ># and #<-1,6,2 >#?
- What is the dot product of #<-5,2,8 ># and #<-1,6,2 >#?
- What is the dot product of #<1,0,-2 ># and #<-1,-4,1 >#?
- What is the dot product of #<-4,-3,8 ># and #<3,-1,7 >#?
- What is the dot product of #<-7,2,-1 ># and #<0,8,-27 >#?
- What is the dot product of #<9,1,-1 ># and #<6,-8,2 >#?
- What is the dot product of #<3,4,1 ># and #<5,-1,2 >#?
- What is the dot product of #<7,1,1 ># and #<-2,4,-8>#?
- What is the dot product of #<7,0,1 ># and #<-2,4,-3>#?
- What is the dot product of #<-4,0,-2 ># and #<3,-9,1>#?
- What is the dot product of #<-4,5,-2># and #<-2,4,1>#?
- What is the dot product of #<1,-4,5 ># and #<-5,7,3 >#?
- What is the dot product of #<5,6,-3 ># and #<-4,8,-5 >#?
- What is the dot product of #<5,4,-4># and #<-4,1,5 >#?
- What is the dot product of #<8,-1,4># and #<9,1,5 >#?
- What is the dot product of #<8,4,1># and #<4,-2,3 >#?
- What is the dot product of #<8,8,1># and #<-1, 2,3 >#?
- What is the dot product of #<-1,-2,1># and #<-1, 2,3 >#?
- What is the dot product of #<7,-8,1># and #<4,-6,3 >#?
- What is the dot product of #<9,4,1># and #<7,6,3 >#?
- What is the dot product of #<9,4,1># and #<-5,1,7 >#?
- What is the dot product of #<2,4,7># and #<1,-7,7 >#?
- What is the dot product of #<2,0,7># and #<-4,9,-1 >#?
- What is the dot product of #<-1,4,7># and #<9,-7,5 > #?
- What is the dot product of #<-6,1,0># and #<2,7,5 > #?
- What is the dot product of #<-6,4,2 > # and #<7,1,0 > #?
- What is the dot product of #<-8,4,2 > # and #<-3,1,6 > #?
- What is the dot product of #<-8,5,2 > # and #<-3,1,7 > #?
- What is the dot product of #<-8,1,2 > # and #<-2,5,-1 > #?
- What is the dot product of #<-8,1,2 > # and #<-2,-8,-1 > #?
- What is the dot product of #<-1,1,2 > # and #<-2,-8,-1 > #?
- What is the projection of #<8,2,1 ># onto #<9,6,3 >#?
- What is the projection of #<-6,2,1 ># onto #<-5,1,3 >#?
- What is the projection of #<7,-5,6 ># onto #<-1,-3,7 >#?
- What is the projection of #<8,-1,6 ># onto #<-1,5,-3 >#?
- What is the projection of #<3,-4,6 ># onto #<-1,7,-3 >#?
- What is the projection of #<6,-4,8 ># onto #<-1,3,-7 >#?
- What is the projection of #<3,4,-1 ># onto #<-1,3,-6 >#?
- What is the projection of #<5,6,1 ># onto #<8,-5,1 >#?
- What is the projection of #<5,8,-2 ># onto #<4,-5,2 >#?
- What is the projection of #<5,0,-2 ># onto #<1,-1,0 >#?
- What is the projection of #<3,-7,4># onto #<1,4,0 >#?
- What is the projection of #<8,-5,3 ># onto #<7,6,0 >#?
- What is the projection of #<6,5,3 ># onto #<2,-1,8 >#?
- What is the projection of #<6,0,3 ># onto #<2,5,-7 >#?
- What is the projection of #<6,-4,9 ># onto #<7,8,7 >#?
- What is the projection of #<2,-5,1 ># onto #<6,-8,3 >#?
- What is the projection of #<2,-7,1 ># onto #<4,-5,9 >#?
- What is the projection of #<2,7,1 ># onto #<3,-5,7 >#?
- What is the projection of #<7,1,1 ># onto #<-1,6,-8 >#?
- What is the projection of #<4,9,1 ># onto #<-1,7,2 >#?
- What is the projection of #<4,0,1 ># onto #<6,-3,7 >#?
- What is the projection of #<-5,3,7 ># onto #<0,8,-2 >#?
- What is the projection of #<-8,3,7 ># onto #<1,4,-3 >#?
- What is the projection of #<-2,3,7 ># onto #<1,6,1 >#?
- What is the projection of #<-2,2,5 ># onto #<1,6,9 >#?
- What is the projection of #<-6,1,5 ># onto #<1,5,9 >#?
- What is the projection of #<4,-6,3 ># onto #<1,5,2 >#?
- What is the projection of #<2,-4,3 ># onto #<1,2,2 >#?
- What is the projection of #<2,4,3 ># onto #<-3,4,-1 >#?
- What is the projection of #<-4,8,9 ># onto #<8,1,-1 >#?
- What is the projection of #<7,-8,3 ># onto #<5,-6,1 >#?
- What is the projection of #<5,8,3 ># onto #<2,4,-2 >#?
- What is the projection of #<-2,3,3 ># onto #<2,-3,2 >#?
- What is the projection of #<-3,5,-9 ># onto #<2,-1,4 >#?
- What is the projection of #<8,2,-6 ># onto #<5,-1,7 >#?
- What is the projection of #<4,-1,6 ># onto #<1,3,-2 >#?
- What is the projection of #<-6,3,2 ># onto #<1,4,-3 >#?
- What is the projection of #<-2,4,2 ># onto #<1,8,-3 >#?
- What is the projection of #<5,-2,3 ># onto #<1,-6,-3 >#?
- What is the projection of #<-5,2,8># onto #<8,-3,3 >#?
- What is the projection of #<-5,2,8># onto #<4,-6,3 >#?
- What is the projection of #<4,-6,8># onto #<4,-6,3 >#?
- What is the norm or #<5,2,-7 >#?
- What is the norm of #<1,-3,-2 >#?
- What is the norm or #<1,6,-1 >#?
- What is the norm or #<-7 ,6,-1 >#?
- What is the norm or #<-7 , 5, 1 >#?
- What is the norm of #< 7 , 5, 1 >#?
- What is the norm or #< 7 , -3 , 2 >#?
- What is the norm or #< 4 , 3 , -2 >#?
- What is the norm or #< 4 , 3 , 9 >#?
- What is the norm or #< 4 , -4 , 9 >#?
- What is the norm or #< 8 ,-4 , 9 >#?
- What is the norm of #< 8 ,-2 , 5 >#?
- What is the norm of #< -5 , 4 , 5 >#?
- What is the norm of #< 5 , 7 , -2 >#?
- What is the norm of #< -3, -4 , -2 >#?
- What is the norm of #< -3, -1 , 8 >#?
- What is the norm of #< -3, -1 , -3 >#?
- What is the norm of #< 5 , -2, 3 >#?
- What is the norm of #< -5 , -2, 4 >#?
- What is the norm of #< -5 , -2, -1 >#?
- What is the norm of #< 7 , -2, -1 >#?
- What is #|| <-3, 6 , 8 > - <5, -2 , 7 > ||#?
- What is #|| <-3, -6 , 8 > - <5, -2 , -3 > ||#?
- What is #|| <-1, -2, 7 > - <3, 2 , -3 > ||#?
- What is #|| <-1, -2, 4 > - < 2, -6, 1 > ||#?
- What is #|| <-1, 7, 4 > - < 2, 1, 1 > ||#?
- What is #|| <-1, 9, -2 > - < 9 , -4, 1 > ||#?
- What is #|| <-1, -9, -2 > - < -2 , -4, 1 > ||#?
- What is #|| <-1, 4, 2 > - < -2 , -7, 3 > ||#?
- What is #|| <7, 3, -1> - < -2 , 5, 3 > ||#?
- What is #|| <-8, 3, -1> - < 4 , -5, 3 > ||#?
- What is #|| <-8, 5, 1> - < 4 , -7, 9 > ||#?
- What is #|| <-3, 5, 1> - < 4 , -7, 4 > ||#?
- What is #|| <-6, 1, -3 > - < 4 , 6, 5 > ||#?
- What is #|| <-7, 31, -3 > - < 4 , 4, -1 > ||#?
- What is #|| <-7, -7, -3 > - < 4 , 4, -1 > ||#?
- What is #|| <-9, 3, 3 > - < 6, -2, 1 > ||#?
- What is #|| <-9, 3, 3 > - < 9, -2, 1 > ||#?
- What is #|| <4, 5, -7 > - < 9, -2, 1 > ||#?
- What is #|| <4, 9, 7 > - < 9, -1, 2> ||#?
- What is #|| <1, 9, 7 > - < 2, -1, 2> ||#?
- What is #|| <1, 9, 7 > - < 4, -2, -9 >||#?
- What is #|| <1, 6, -3 > - < 4, -2, -9 >||#?
- What is # || < 5 , -6 , 9> + < 2 , -4, -7 > || #?
- What is # || < 5 , 3, -3 > || #?
- What is # || < -6 , 3, -3 > || #?
- What is # || < -6 , -7 , -3 > || #?
- What is #||<< -6,-7,1 >>||# (the magnitude of #<< -6, -7, 1 >>#)?
- What is # || < -2 , -7 , 1 > || #?
- What is # || < -2 , 3 , 1 > || #?
- What is # || < -2 , 3 , 6 > || #?
- What is # || < 9 , 1 , 6 > || #?
- What is # || < -4 , 1 , 6 > || #?
- What is # || < -4 , 8 , 6 > || #?
- What is # || < -4 , 8 , -5 > || #?
- What is # || < 4 , -3 , -8 > || #?
- What is # || < 4 , 9 , -8 > || #?
- What is # || < -3, 9 , 5 > || #?
- What is # || < -3, -3, 0 > || #?
- What is # || < -3, -3, 0 > || #?
- What is # || < 3, 4 , 0 > || #?
- What is the cross product of #<6,-2,8 ># and #<1,3,-4 >#?
- What is the cross product of #<9,2,8 ># and #<1,3,-4 >#?
- What is the cross product of #<9,2,8 ># and #<1,8,4 >#?
- What is the cross product of #<9,2,8 ># and #<6, -2, 7 >#?
- What is the cross product of #<-3,5,8 ># and #<6, -2, 7 >#?
- What is the cross product of #<-3,5,8 ># and #<6, -2, 7 >#?
- What is the cross product of #<-3,5,8 ># and #<-9,3,1>#?
- What is the cross product of #<-3,4, 8 ># and #<-9,3,1>#?
- What is the cross product of #<-3,4, 8 ># and #<2,-4, 1>#?
- What is the cross product of #<-3,4, 8 ># and #<2,-4, -9 >#?
- What is the cross product of #<-3, -1, 8 ># and #<2,-4, -9 >#?
- What is the cross product of #<-3, -1, 8 ># and #<-1, 4, -9 >#?
- What is the cross product of #<-3,0, 8 ># and #<-1, -2, 9 >#?
- What is the cross product of #<-3,0, 2># and #<-1, -2, 9 >#?
- What is the cross product of #<-3,0, 2># and #<-1, -4, 1>#?
- What is the cross product of #<8, 4 ,-2 ># and #<-1, -4, 1>#?
- What is the cross product of #<8, 4 ,-2 ># and #<-1, -1, 6 >#?
- What is the cross product of #<8, 4 ,-2 ># and #<-1, 3 ,2 >#?
- What is the cross product of #<-2, 5 ,-2 ># and #<-1, 3 ,2 >#?
- What is the cross product of #<-2, 5 ,-2 ># and #<-1, -9 ,2 >#?
- What is the cross product of #<-2, 5 ,-2 ># and #<7 , -9 ,2 >#?
- What is the cross product of #<-2, 5 ,-2 ># and #<7 ,3 ,2 >#?
- What is the cross product of #<-2, -1 ,-6 ># and #<7 ,3 ,2 >#?
- What is the cross product of #<3 ,1 ,-6 ># and #<7 ,3 ,2 >#?
- What is the cross product of #<3 ,1 ,-6 ># and #<-2 ,3 ,2 >#?
- What is the cross product of #<3 ,1 ,-6 ># and #<-2 ,-4 , 8 >#?
- What is the cross product of #<3 ,1 ,-6 ># and #<-2 ,1 , 8 >#?
- What is the cross product of #<3 ,-4 ,-3 ># and #<-2 ,1 , -7 >#?
- What is the cross product of #<-3 ,-6 ,-3 ># and #<-2 ,1 , -7 >#?
- What is the cross product of #<-3 ,-6 ,-3 ># and #<0 ,1 , -7 >#?
- What is the cross product of #<< -3,-6,-3 >># and #<< -5,2,-7 >>#?
- What is the cross product of #<7 ,4 ,-3 ># and #<-5 ,2 , -7 >#?
- What is the cross product of #<7 ,4 ,1 ># and #<-5 ,2 ,8 >#?
- What is the cross product of #<0 ,4 ,1 ># and #<-5 ,2 ,8 >#?
- What is the cross product of #<10 ,4 ,1 ># and #<-5 ,2 ,3 >#?
- What is the cross product of #<5, -3,1 ># and #<-5 ,2 ,3 >#?
- What is the cross product of #<5, -3,1 ># and #<-2 ,2 ,3 >#?
- What is the cross product of #<5, -3, 8 ># and #<-2 ,7 ,3 >#?
- What is the cross product of #<5, 2 , 8 ># and #<4 ,7 ,3 >#?
- What is the cross product of #<5, 2 ,5 ># and #<4 ,7 ,3 >#?
- What is the cross product of #<5, 2 ,5 ># and #<4 ,1 ,3 >#?
- What is the cross product of #<5, 2 ,5 ># and #<4 ,1 ,9 >#?
- What is the cross product of #<5, 2 ,15 ># and #<4 ,1 ,9 >#?
- What is the cross product of #<-1, 2 ,0 ># and #<-3 ,1 ,9 >#?
- What is the cross product of #<-1, 2 ,7 ># and #<-3 ,1 ,4 >#?
- What is the cross product of #<-1, 2 ,7 ># and #<-3 ,1 ,-1 >#?
- What is the cross product of #<-1, 2 ,27 ># and #<-3 ,1 ,-1 >#?
- What is the cross product of #<7, 2 ,5 ># and #<-3 ,1 ,-6 >#?
- What is the cross product of #<7, 2 ,6 ># and #<-3 ,5 ,-6 >#?
- What is the cross product of #<7, 5 ,6 ># and #<3 ,5 ,-6 >#?
- What is the cross product of #<7, 5 ,6 ># and #<3 ,5 ,-2 >#?
- What is the cross product of #<2 , 5 ,-3 ># and #<3 ,5 ,-2 >#?
- What is the cross product of #<2 , 5 ,-3 ># and #<5 ,6 ,-2 >#?
- What is the cross product of #<2 , 5 ,-7 ># and #<5 ,6 ,-9 >#?
- What is the cross product of #<5 , 5 ,-7 ># and #<5 ,6 ,-3 >#?
- What is the cross product of #<5 , 5 ,-7 ># and #<5 ,1 ,-3 >#?
- What is the cross product of #<4 , 5 ,-7 ># and #<5 ,1 ,-3 >#?
- What is the cross product of #<4 , 5 ,-9 ># and #<5 ,1 ,-3 >#?
- What is the cross product of #<4 , 5 ,-9 ># and #<5 ,-3 ,-3 >#?
- What is the cross product of #<4 , 5 ,-9 ># and #<4, 3 ,-3 >#?
- What is the cross product of #<4 , 5 ,-9 ># and #<4, 3 ,0 >#?
- What is the cross product of #<4 , 5 ,-9 ># and #<4, 8 ,-2 >#?
- What is the cross product of #<4 , 5 ,-9 ># and #<4, 1 ,-2 >#?
- What is the cross product of #<4 , 5 ,0 ># and #<4, 1 ,-2 >#?
- What is the component form of a vector with an initial point of (-2, 3) and a terminal point of (-4, 7)?
- The resultant of the two forces #3N# and#2N# at an angle #theta# is doubled when first force in increased to #6N#. Find #theta#?
- Question #aecf3
- Consider the angle sum formulas: #sin(A+B)=sinA cosB+cosA sinB# #cos(A+B)=cosA cosB−sinA sinB# show that #tan(90^0+θ)=− 1/tanθ#. and use this identity to prove that lines #y = mx and y = m_1x# are perpendicular iff #mm_1=−1#?
- Question #74c1d
- Question #ae8d8
- Question #848d3
- Question #89967
- How will you prove the trigonometric formula #cos(A+B)=cosAcosB-sinAsinB# by using formula of cross product of two vectors ?
- How will you prove the formula #sin(A+B)=sinAcosB+cosAsinB# using formula of scalar product of two vectors?
- How will you prove the formula #sin(A-B)=sinAcosB-cosAsinB# using formula of scalar product of two vectors?
- How will you prove the formula #cos(A-B)=cosAcosB+sinAsinB# using formula of vector product of two vectors?
- Question #be172
- Question #d7dc2
- Question #d3574
- What is the direction of null vector?
- What is the angle between two forces of equal magnitude, #F_a# and #F_b#, when the magnitude of their resultant is also equal to the magnitude of either of these forces?
- Question #c976d
- Question #8f4d7
- Question #e27ab
- Question #84ddc
- Determine unit vector which is perpendicular to both A=2i+j+k and B=i-j+2k?
- Question #4760f
- Question #c380e
- Question #15905
- Question #4bd8a
- Question #b8942
- Question #1b250
- Can a vector have a negative component?
- What is the value of #(A #x# B)^2# + #(A * B)^2# ?
- Question #4acab
- Question #e748d
- Question #82dbe
- Question #960ba
- Why is vector division not possible?
- Question #a16d3
- Question #fc58a
- Question #5d77a
- A farmer wants to wall off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in the figure, where A = 4.99 km, B = 2.46 km, and C = 3.23 km and then correctly calculates the length and orientation of D?
- Question #2a277
- Why does multiplication of vectors not have a corresponding division?
- Question #1f88b
- Question #a42a8
- Question #2d7d4
- Question #89959
- Question #4dd1c
- Question #276ee
- Question #18491
- Question #987b7
- Question #5c77f
- Question #795a2
- Question #5b790
- Question #0b785
- If A= A1i + A2j + A3k and B= B1i + B2j + B3k. Prove that A.B= A1B1+A2B2+A3B3?
- Question #fca5d
- Question #17931
- Sarah can paddle a rowboat at 6 m/s in still water. She heads out across a 400 m river at an angle of 30 upstream. She reaches the other bank of the river 200 m downstream from the direct opposite point from where she started. Determine the river current?
- Question #50b52
- Question #26a9b
- If we assume that the definition of the inner product of the normalized vectors #hatu_1# and #hatu_2# is #2u_1^2 + u_2^2# (these are vector components), how do you use the Gram-Schmidt process to generate orthonormal vectors from #vecv_1# and #vecv_2#?
- Question #834e1