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 = (11, 3).

a = (11, 3)
|a| =
2.Easy
xy70°F = 160 N

A force of 160 N acts in the xy-plane at 70° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 160 Nθ = 70°
Fx = N
3.Medium
xyzab

Find the scalar projection compb a of a = (4, −5, 3) onto b = (−3, 6, −2), that is, the component of a in the direction of b.

a = (4, −5, 3)b = (−3, 6, −2)
compb a =
4.Medium
xyzab

Find the angle θ between the vectors a = (0, 6, −2) and b = (−1, 4, 4), in degrees.

a = (0, 6, −2)b = (−1, 4, 4)
θ = °
5.Hard
xyzrFOA

A force F = (10, −40, 50) N acts at point A(−1, −1, 3). Coordinates are in metres. Find the y-component My of the moment of the force about point O(2, 1, −2).

F = (10, −40, 50) NA(−1, −1, 3) mO(2, 1, −2) m
My = N·m
6.Hard
xyzab

For a = (−5, −2, −1) and b = (−1, −6, −4), find the y-component (a × b)y of the cross product a × b.

a = (−5, −2, −1)b = (−1, −6, −4)
(a × b)y =

Answer key

  1. 1. |a| = 11.4
  2. 2. Fx = 54.72 N
  3. 3. compb a = −6.857
  4. 4. θ = 63.87 °
  5. 5. My = 200 N·m
  6. 6. (a × b)y = −19

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