Vectors: dot & cross product worksheet with answers

Free printable Vectors: dot & cross product worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xyza

Find the x-component ûx of the unit vector û that points in the direction of a = (−1, −1, −7).

a = (−1, −1, −7)
ûx =
2.Easy
xy185°F = 80 N

A force of 80 N acts in the xy-plane at 185° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 80 Nθ = 185°
Fx = N
3.Medium
xyzab

Find the scalar projection compb a of a = (4, −4, −2) onto b = (−6, −5, −1), that is, the component of a in the direction of b.

a = (4, −4, −2)b = (−6, −5, −1)
compb a =
4.Medium
xyzab

Find the value of k for which the vectors a = (6, −4, 3) and b = (k, −3, 4) are perpendicular.

a = (6, −4, 3)b = (k, −3, 4)
k =
5.Hard
xyzrFOA

A force F = (−50, 60, 10) N acts at point A(−4, 3, 2). Coordinates are in metres. Find the y-component My of the moment of the force about point O(−2, −2, −1).

F = (−50, 60, 10) NA(−4, 3, 2) mO(−2, −2, −1) m
My = N·m
6.Hard
xyzab

For a = (−4, −2, −1) and b = (5, 0, −5), find the z-component (a × b)z of the cross product a × b.

a = (−4, −2, −1)b = (5, 0, −5)
(a × b)z =

Answer key

  1. 1. ûx = −0.14
  2. 2. Fx = −79.7 N
  3. 3. compb a = −0.254
  4. 4. k = −4
  5. 5. My = −130 N·m
  6. 6. (a × b)z = 10

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