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
xya

Find the magnitude |a| of the vector a = (12, 4).

a = (12, 4)
|a| =
2.Easy
xy175°F = 470 N

A force of 470 N acts in the xy-plane at 175° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 470 Nθ = 175°
Fx = N
3.Medium
xyzab

Find the value of k for which the vectors a = (2, 3, 3) and b = (4, −6, k) are perpendicular.

a = (2, 3, 3)b = (4, −6, k)
k =
4.Medium
xyzab

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

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

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

a = (1, −4, −4)b = (−1, 2, 0)
(a × b)y =
6.Hard
xyzrFOA

A force F = (50, 40, 60) N acts at point A(−1, 4, 1). Coordinates are in metres. Find the magnitude |M| of the moment of the force about point O(2, −1, −3).

F = (50, 40, 60) NA(−1, 4, 1) mO(2, −1, −3) m
|M| = N·m

Answer key

  1. 1. |a| = 12.65
  2. 2. Fx = −468.2 N
  3. 3. k = 3.333
  4. 4. compb a = −7.715
  5. 5. (a × b)y = 4
  6. 6. |M| = 548.5 N·m

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