# Vector Operations

### Topic Page

Vector Operations### Questions

- Question #b4ef9
- What is meant by a component of a vector?
- How do I find the vertical component of a vector?
- How do i find the horizontal component of a vector?
- Is vector addition commutative?
- What happens when I multiply a vector by itself?
- What is the definition of vector addition?
- How do I do vector subtraction?
- What is a velocity vector?
- How can the law of cosines be used to find the magnitude of a resultant?
- Can the sum of three vectors be zero?
- How do I find the sum of three vectors?
- How to find a vector A that has the same direction as ⟨−8,7,8⟩ but has length 3 ?
- If ||v|| = 3, what is ||-2v||?
- The vector v has initial point P and terminal point Q. How do you write v in the form ai + bj, that is, find its position vector given P = (5, 4); Q = (7, 8)?
- How do you find ||v|| given v = i - j?
- How do you write the vector a = 3i + 2j - 6k as a sum of two vectors, one parallel and one perpendicular to d = 2i - 4j + k?
- Vector A has length 24.9 and is at an angle of 30 degrees. Vector B has length 20 and is at an angle of 210 degrees. To the nearest tenth of a unit, what is the magnitude of A+B?
- A boat travelling at 6 m/s heads due north across a 106 meter wide river. If the east flowing current in the river is 2.5 m/s,to the nearest meter, how far east of it's starting position is the boat when it reaches the north shore?
- A baseball is hit off a 1 meter high tee at an angle of 36.9 degrees and at a speed of 27.4 m/s.How far to the nearest tenth of a meter does it travel horizontally?
- A golf ball is launched at a 30 degree angle with a speed of 46 m/s.To the nearest tenth of a meter, what is its maximum height?
- A football is kicked at an angle of 45 degrees from a distance of 34 meters and just clears a 3 meter high goal on its way down. To the nearest m/s what was its initial speed?
- An airplane travelling horizontally at 406 km/h at a height of 2 km releases a bomb. How far ahead (to the nearest meter) from the release point does the bomb strike the ground?
- A seagull diving towards a stone beach at an angle of 60 degrees to the vertical releases a clam from a height of 100 meters. The clam hits the beach seconds later. To the nearest tenth of a 2.32 m/s what was its speed when it was released?
- Given two vectors A= 4.00i +3.00j and B= 5.00i -2.00j , how do you find the vector product A times B (expressed in unit vectors)?
- Vector A points to the north and has length A. Vector B points to the east and has length B=2.0A. How do you find the magnitude of C=3.6A+B in terms of A?
- How do you find the cross product a × b given #a = ‹t,t^2,t^3›#, #b = ‹1, 6t, 8t^2› #?
- Given the displacement vectors #A= (3i – 4j + 4k)m#, and #B= (2i + 3j – 7k)m#, how do you find the magnitudes of the vectors #C= A+B#?
- Vector A has a magnitude of 13 units at a direction of 250 degrees and vector B has a magnitude of 27 units at 330 degrees, both measured with respect to the positive x axis. What is the sum of A and B?
- A vector A has a magnitude of 48.0 m and points in a direction 20° below the positive x axis. A second vector, B, has a magnitude of 75 m and points in a direction 60.0° above the positive x axis?
- Given A (2,-1,1) , B (3,0,5), C (1,4,-2), what is Vector A + Vector B + Vector C?
- Two vectors are given by a = 3.3 x - 6.4 y and b = -17.8 x + 5.1 y. What is the magnitude of a?
- Two vectors are given by a = 3.3 x - 6.4 y and b = -17.8 x + 5.1 y. What is the angle between vector b and the positive x-axis?
- Two vectors are given by a = 3.3 x - 6.4 y and b = -17.8 x + 5.1 y. What is the magnitude of the vector a + b?
- Consider two vectors #A=3i - 1j# and #B = - i - 5j#, how do you calculate #A + B#?
- Consider two vectors A=3i - 1j and B = - i - 5j, how do you calculate A - B?
- Consider two vectors A=3i - 1j and B = - i - 5j, how do you calculate #abs(A+B)#??
- Consider two vectors A=3i - 1j and B = - i - 5j, how do you calculate #abs(A-B)#?
- Consider two vectors A=3i - 1j and B = - i - 5j, what is the direction of A + B?
- Consider two vectors A=3i - 1j and B = - i - 5j, what is the direction of A - B?
- Let vectors A=(1,0,-3) ,B=(-2,5,1) and C=(3,1,1), how do you calculate A-B?
- Let vectors A=(1,0,-3) ,B=(-2,5,1) and C=(3,1,1), how do you calculate B-C?
- Let vectors A=(1,0,-3) ,B=(-2,5,1) and C=(3,1,1), how do you calculate (-A)+B-C?
- Let vectors A=(1,0,-3) ,B=(-2,5,1) and C=(3,1,1), how do you calculate 3A-2C?
- Let vectors A=(1,0,-3) ,B=(-2,5,1) and C=(3,1,1), how do you calculate 2A-3(B-C)?
- The position vector of A has the Cartesian coordinates (20,30,50). The position vector of B has the Cartesian coordinates (10,40,90). What are the coordinates of the position vector of A+B?
- Given u=(2,5) v=(-2,1), how do you find |u-v|?
- How do you find the magnitude of the resultant of the vectors A=12x-37y+52z and B=5x+30y-42z. where i, j, and k are unit vectors along the x, y and z axes respectively?
- A car is driven 215 km west and then 85 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?
- Question #07b7f
- Vector A has a magnitude of 10 and points in the positive x-direction. Vector B has a magnitude of 15 and make an angle of 34 degrees with the positive x-axis. What is the magnitude of A - B?
- A vector F1 = 500 N due east and another F2 =250 N due north are on a plane. How do you find F2-F1?
- Given Vector A: 15cm at zero degrees and Vector B: 30cm at 60 degrees, How do you add and subtract these two vectors?
- Given Vector A: 10cm at 240 degrees, Vector B: 20cm at 135 degrees, Vector C: 15 cm at 30 degrees. How do you add and subtract these three vectors?
- Given Vector A: 14.1i + 5.1j and Vector B: 15.0i + 26.0j. How do you add and subtract these two vectors?
- Given Vector A: 25.2cm at 81.6 degrees and Vector B: 32.1 cm at 142.7 degrees. How do you add and subtract these two vectors?
- Given Vector E=4i+2j and Vector F=6i-10j, How do you add and subtract these two vectors?
- Vector A=125 m/s, 40 degrees north of west. Vector B is 185 m/s, 30 degrees south of west and vector C is 175 m/s 50 east of south. How do you find A+B-C by vector resolution method?
- How do you subtract vectors given V1 = -5i + 2j and V2 = -3i -9j?
- Question #16ef7
- Question #f4b39
- Given a #triangleABC# with #a=10#, #b=20# and #/_C=95^circ#, what are the lengths of all sides and size of all angles?
- How do you find u+v and u-v given u=<2,1> and v=<1,3>?
- How do you find u+v and u-v given u=<-5,3> and v=<0,0>?
- How do you find u+v and u-v given u=i+j and v=2i-3j?
- How do you find u+v and u-v given u=2i and v=j?
- How do you find an ordered pair to represent u+v given u=<-1,4> and v=<3,-2>?
- How do you find an ordered pair to represent 1/2u-v given u=<-1,4> and v=<3,-2>?
- How do you find an ordered pair to represent #4u+6v# given #u=<-1,4># and #v=<3,-2>#?
- How do you find an ordered pair to represent -8u given u=<-1,4> and v=<3,-2>?
- How do you find the magnitude of <8,-6>?
- How do you find the magnitude of <-7, -5>?
- How do you find the magnitude of YZ given Y(4,2) and Z(2,8)?
- How do you find the magnitude of YZ given Y(-5,7) and Z(-1,2)?
- How do you find the magnitude of YZ given Y(-2,5) and Z(1,3)?
- How do you find the magnitude of YZ given Y(5,4) and Z(0,-3)?
- How do you find the magnitude of YZ given Y(3,1) and Z(0,4)?
- How do you find the magnitude of YZ given Y(-4,12) and Z(1,19)?
- How do you find the magnitude of YZ given Y(5,0) and Z(7,6)?
- How do you find the magnitude of YZ given Y(14,-23) and Z(23, -14)?
- How do you find a=b+c given b=<6,3> and c=<-4,8>?
- How do you find a=2b+c given b=<6,3> and c=<-4,8>?
- How do you find a=b+2c given b=<6,3> and c=<-4,8>?
- How do you find a=2b+3c given b=<6,3> and c=<-4,8>?
- How do you find a=-b+4c given b=<6,3> and c=<-4,8>?
- How do you find a=b-2c given b=<6,3> and c=<-4,8>?
- How do you find a=3b given b=<6,3> and c=<-4,8>?
- How do you find a=-1/2c given b=<6,3> and c=<-4,8>?
- How do you find a=6b+4c given b=<6,3> and c=<-4,8>?
- How do you find a=0.4b-1.2c given b=<6,3> and c=<-4,8>?
- How do you find a=1/3(2b-5c) given b=<6,3> and c=<-4,8>?
- How do you find #a=(3b+c)+5b# given #b=<6,3># and #c=<-4,8>#?
- How do you find the magnitude <3,4>?
- How do you find the magnitude <2,-3>?
- How do you find the magnitude <-6,-11>?
- How do you find the magnitude <3.5, 12>?
- How do you find the magnitude <-4,1>?
- How do you find the magnitude <-16,-34>?
- How do you find u=6w+2z given v=<4,-3,5>, w=<2,6,-1> and z=<3,0,4>?
- How do you find #u=1/2v-w+2z# given v=<4,-3,5>, w=<2,6,-1> and z=<3,0,4>?
- How do you find #u=3/4v-w# given v=<4,-3,5>, w=<2,6,-1> and z=<3,0,4>?
- How do you find #u=3v-2/3w+2z# given v=<4,-3,5>, w=<2,6,-1> and z=<3,0,4>?
- How do you find #u=0.75v+0.25w# given v=<4,-3,5>, w=<2,6,-1> and z=<3,0,4>?
- How do you determine if the vectors are coplanar: a = [-2,-1,4], b = [5,-2,5], and c = [3,0,-1]?
- How do you use the definition of the scalar product, find the angles between the following pairs of vectors: A = -i - 2k and B = - 5i + 5j + 5k?
- How do you use the definition of the scalar product, find the angles between the following pairs of vectors: A = - 2j -5k and B = - 4i + j - 4k?
- How do you use the definition of the scalar product, find the angles between the following pairs of vectors: A = 3i + 4j - 4k and B= 4i - 5j + 5k?
- How do you find a vector perpendicular to the vectors v=(1 3 -2) and u=(1 2 -2)?
- Question #13832
- Is there an infinite dimensional vector space #H# with bounded linear operator from #H# onto #H# which preserves the inner product?
- Can the magnitude of a vector be negative?
- How do you find the magnitude of #<5,6># and write it as a sum of the unit vectors?
- How do you find the magnitude of #<-2,4># and write it as a sum of the unit vectors?
- How do you find the magnitude of #<-10,-5># and write it as a sum of the unit vectors?
- How do you find the magnitude of <2.5,6> and write it as a sum of the unit vectors?
- How do you find the magnitude of <2,-6> and write it as a sum of the unit vectors?
- How do you find the magnitude of <-15,-12> and write it as a sum of the unit vectors?
- How do you find the inner product and state whether the vectors are perpendicular given #<3,4>*<2,5>#?
- How do you find the inner product and state whether the vectors are perpendicular given #<-3,2>*<4,6>#?
- How do you find the inner product and state whether the vectors are perpendicular given #<-5,3>*<2,-3>#?
- How do you find the inner product and state whether the vectors are perpendicular given #<8,6>*<-2,-3>#?
- How do you find the inner product and state whether the vectors are perpendicular given #<3,4,0>*<4,-3,6>#?
- How do you find the inner product and state whether the vectors are perpendicular given #<4,5,1>*<-1,-2,3>#?
- How do you find the cross product and state whether the resulting vectors are perpendicular to the given vectors #<3,0,4>times<-1,5,2>#?
- How do you find the cross product and state whether the resulting vectors are perpendicular to the given vectors #<-1,1,0>times<2,1,3>#?
- How do you find the cross product and state whether the resulting vectors are perpendicular to the given vectors #<-1,-3,2>times<6,-1,-2>#?
- Use the Law of Sines to solve the triangle? 6.) A=60 degrees, a=9, c=10.
- ) Suppose the relationship Projau = Projav is true for some vectors a, u and w. (i) Verify that u · v = v · a. (5) (ii) Provide a counter example to show that u need not be equal to v in your example?
- Question #807f7
- Is the set of all vectors in #R2# of the form #(a, b)# where #b = a# closed under addition?
- Question #3aaaa
- Let say K and L are two different subspace real vector space #V#. If given #dim(K)=dim(L)=4#, how to determine minimal dimensions are possible for #V# ?
- If # bb(ul u) = << −1,0,2 >> #, # bb(ul v) = << 3,1,2 >> # and # bb(ul w) = << 1,−2,−2 >> # then find?
- What is the euclidean norm?
- Determine the value(s) of k such that (2k, 3, k+1) x (k-1, k, 1) = (1, -2, 2)?
- #bb(ul hata)#, #bb(ul hatb)# and #bb(ul hatc)# are unit vectors, and the angle between #bb(ul hatb)# and #bb(ul hatc)# is #pi/6#. Show that # bb(ul hata) = +-2 (bb(ul hatb) xx bb(ul hatc))#?
- What is the dot product of a vector and #<<1, 1, 1 >>#?