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
xyza

Find the magnitude |a| of the vector a = (7, 9, 1).

a = (7, 9, 1)
|a| =
2.Easy
xyza

Find the magnitude |a| of the vector a = (−2, −8, 4).

a = (−2, −8, 4)
|a| =
3.Medium
xyzdFAB

A constant force F = (−15, 0, 30) N acts on an object while it moves in a straight line from point A(−1, 1, −4) to point B(2, 5, 5). Coordinates are in metres. Find the work W done by the force.

F = (−15, 0, 30) NA(−1, 1, −4) mB(2, 5, 5) m
W = J
4.Medium
xyzab

Find the angle θ between the vectors a = (−5, 4, 4) and b = (3, −1, 4), in degrees.

a = (−5, 4, 4)b = (3, −1, 4)
θ = °
5.Hard
xyzabc

Find the volume V of the parallelepiped whose edges from one corner are a = (2, 0, 1), b = (−1, 5, −3) and c = (0, 3, −3).

a = (2, 0, 1)b = (−1, 5, −3)c = (0, 3, −3)
V =
6.Hard
xyzab

Find the area A of the parallelogram spanned by a = (3, 2, 5) and b = (5, 6, 0).

a = (3, 2, 5)b = (5, 6, 0)
A =

Answer key

  1. 1. |a| = 11.45
  2. 2. |a| = 9.165
  3. 3. W = 225 J
  4. 4. θ = 94.47 °
  5. 5. V = 15
  6. 6. A = 39.86

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