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
xy80°F = 210 N

A force of 210 N acts in the xy-plane at 80° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 210 Nθ = 80°
Fx = N
2.Easy
xy115°F = 220 N

A force of 220 N acts in the xy-plane at 115° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 220 Nθ = 115°
Fx = N
3.Medium
xyzab

Find the value of k for which the vectors a = (−5, 1, −2) and b = (0, 3, k) are perpendicular.

a = (−5, 1, −2)b = (0, 3, k)
k =
4.Medium
xyzab

Find the angle θ between the vectors a = (3, −6, −6) and b = (−4, −3, −4), in degrees.

a = (3, −6, −6)b = (−4, −3, −4)
θ = °
5.Hard
xyzabc

Find the volume V of the parallelepiped whose edges from one corner are a = (4, −5, −3), b = (−4, 3, −5) and c = (3, 2, −2).

a = (4, −5, −3)b = (−4, 3, −5)c = (3, 2, −2)
V =
6.Hard
xyzrFOA

A force F = (40, −40, −60) N acts at point A(−4, 3, −3). Coordinates are in metres. Find the y-component My of the moment of the force about the origin O(0, 0, 0).

F = (40, −40, −60) NA(−4, 3, −3) mO(0, 0, 0) m
My = N·m

Answer key

  1. 1. Fx = 36.47 N
  2. 2. Fx = −92.98 N
  3. 3. k = 1.5
  4. 4. θ = 58.63 °
  5. 5. V = 182
  6. 6. My = −360 N·m

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