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 = (4, 9).

a = (4, 9)
|a| =
2.Easy
xyza

Find the magnitude |a| of the vector a = (−7, 3, 5).

a = (−7, 3, 5)
|a| =
3.Medium
xyzdFAB

A constant force F = (5, 30, 20) N acts on an object while it moves in a straight line from point A(1, 2, −2) to point B(2, 2, −5). Coordinates are in metres. Find the work W done by the force.

F = (5, 30, 20) NA(1, 2, −2) mB(2, 2, −5) m
W = J
4.Medium
xyzab

Find the angle θ between the vectors a = (−2, 6, −1) and b = (5, −1, −4), in degrees.

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

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

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

Find the volume V of the parallelepiped whose edges from one corner are a = (−2, −5, 1), b = (−2, 0, 5) and c = (−2, −3, 4).

a = (−2, −5, 1)b = (−2, 0, 5)c = (−2, −3, 4)
V =

Answer key

  1. 1. |a| = 9.849
  2. 2. |a| = 9.11
  3. 3. W = −55 J
  4. 4. θ = 106.8 °
  5. 5. V = 5
  6. 6. V = 14

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