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
xy345°F = 400 N

A force of 400 N acts in the xy-plane at 345° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 400 Nθ = 345°
Fx = N
2.Easy
xy80°F = 450 N

A force of 450 N acts in the xy-plane at 80° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 450 Nθ = 80°
Fx = N
3.Medium
xyzdFAB

A constant force F = (−10, −10, 15) N acts on an object while it moves in a straight line from point A(−3, −2, −3) to point B(5, 5, −3). Coordinates are in metres. Find the work W done by the force.

F = (−10, −10, 15) NA(−3, −2, −3) mB(5, 5, −3) m
W = J
4.Medium
xyzdFAB

A constant force F = (−5, 5, 15) N acts on an object while it moves in a straight line from point A(−4, −1, −4) to point B(−3, 3, 0). Coordinates are in metres. Find the work W done by the force.

F = (−5, 5, 15) NA(−4, −1, −4) mB(−3, 3, 0) m
W = J
5.Hard
xyzrFOA

A force F = (−10, −40, −40) N acts at point A(−1, −1, 1). Coordinates are in metres. Find the z-component Mz of the moment of the force about the origin O(0, 0, 0).

F = (−10, −40, −40) NA(−1, −1, 1) mO(0, 0, 0) m
Mz = N·m
6.Hard
xyzabc

Find the volume V of the parallelepiped whose edges from one corner are a = (−2, −3, 0), b = (2, 4, −4) and c = (0, −4, −1).

a = (−2, −3, 0)b = (2, 4, −4)c = (0, −4, −1)
V =

Answer key

  1. 1. Fx = 386.4 N
  2. 2. Fx = 78.14 N
  3. 3. W = −150 J
  4. 4. W = 75 J
  5. 5. Mz = 30 N·m
  6. 6. V = 34

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