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
xy225°F = 390 N

A force of 390 N acts in the xy-plane at 225° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 390 Nθ = 225°
Fx = N
2.Easy
xy225°F = 460 N

A force of 460 N acts in the xy-plane at 225° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 460 Nθ = 225°
Fx = N
3.Medium
xyzdFAB

A constant force F = (10, 15, 10) N acts on an object while it moves in a straight line from point A(−4, 3, −2) to point B(4, −1, 2). Coordinates are in metres. Find the work W done by the force.

F = (10, 15, 10) NA(−4, 3, −2) mB(4, −1, 2) m
W = J
4.Medium
xyzab

Find the dot product a·b of a = (3, 4, 1) and b = (−6, 5, 2).

a = (3, 4, 1)b = (−6, 5, 2)
a·b =
5.Hard
xyzab

The unit vector n̂ is perpendicular to both a = (2, −1, −5) and b = (3, −1, −1) and has a positive z-component. Find its x-component n̂x.

a = (2, −1, −5)b = (3, −1, −1)n̂z > 0
n̂x =
6.Hard
xyzabc

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

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

Answer key

  1. 1. Fx = −275.8 N
  2. 2. Fx = −325.3 N
  3. 3. W = 60 J
  4. 4. a·b = 4
  5. 5. n̂x = −0.2933
  6. 6. V = 80

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