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
xy330°F = 40 N

A force of 40 N acts in the xy-plane at 330° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 40 Nθ = 330°
Fx = N
2.Easy
xyza

Find the y-component ûy of the unit vector û that points in the direction of a = (−4, 6, −7).

a = (−4, 6, −7)
ûy =
3.Medium
xyzab

Find the scalar projection compb a of a = (−1, 0, −7) onto b = (1, 4, −1), that is, the component of a in the direction of b.

a = (−1, 0, −7)b = (1, 4, −1)
compb a =
4.Medium
xyzab

Find the scalar projection compb a of a = (6, 4, −1) onto b = (0, −4, −5), that is, the component of a in the direction of b.

a = (6, 4, −1)b = (0, −4, −5)
compb a =
5.Hard
xyzab

For a = (−1, −4, −4) and b = (6, −1, 3), find the y-component (a × b)y of the cross product a × b.

a = (−1, −4, −4)b = (6, −1, 3)
(a × b)y =
6.Hard
xyzrFOA

A force F = (40, 20, 60) N acts at point A(−3, −2, −2). Coordinates are in metres. Find the magnitude |M| of the moment of the force about the origin O(0, 0, 0).

F = (40, 20, 60) NA(−3, −2, −2) mO(0, 0, 0) m
|M| = N·m

Answer key

  1. 1. Fx = 34.64 N
  2. 2. ûy = 0.597
  3. 3. compb a = 1.414
  4. 4. compb a = −1.718
  5. 5. (a × b)y = −21
  6. 6. |M| = 129.6 N·m

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