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
xy305°F = 490 N

A force of 490 N acts in the xy-plane at 305° measured anticlockwise from the positive x-axis. Find its y-component Fy.

F = 490 Nθ = 305°
Fy = N
2.Easy
xyza

Find the magnitude |a| of the vector a = (−9, 6, 7).

a = (−9, 6, 7)
|a| =
3.Medium
xyzab

Find the value of k for which the vectors a = (5, 4, 5) and b = (−3, 6, k) are perpendicular.

a = (5, 4, 5)b = (−3, 6, k)
k =
4.Medium
xyzab

Find the angle θ between the vectors a = (4, 2, 5) and b = (2, 0, −5), in degrees.

a = (4, 2, 5)b = (2, 0, −5)
θ = °
5.Hard
xyzabc

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

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

For a = (5, 4, −5) and b = (−4, −5, 1), find the z-component (a × b)z of the cross product a × b.

a = (5, 4, −5)b = (−4, −5, 1)
(a × b)z =

Answer key

  1. 1. Fy = −401.4 N
  2. 2. |a| = 12.88
  3. 3. k = −1.8
  4. 4. θ = 118.1 °
  5. 5. V = 67
  6. 6. (a × b)z = −9

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