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 = (−8, 2, 7).

a = (−8, 2, 7)
|a| =
2.Easy
xya

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

a = (−9, 7)
|a| =
3.Medium
xyzab

Find the value of k for which the vectors a = (−1, 3, 4) and b = (k, −6, −1) are perpendicular.

a = (−1, 3, 4)b = (k, −6, −1)
k =
4.Medium
xyzab

Find the dot product a·b of a = (−2, −4, −1) and b = (1, −7, 5).

a = (−2, −4, −1)b = (1, −7, 5)
a·b =
5.Hard
xyzab

For a = (2, −3, 1) and b = (2, 0, −4), find the z-component (a × b)z of the cross product a × b.

a = (2, −3, 1)b = (2, 0, −4)
(a × b)z =
6.Hard
xyzrFOA

A force F = (60, −50, −40) N acts at point A(−3, 0, −2). Coordinates are in metres. Find the z-component Mz of the moment of the force about the origin O(0, 0, 0).

F = (60, −50, −40) NA(−3, 0, −2) mO(0, 0, 0) m
Mz = N·m

Answer key

  1. 1. |a| = 10.82
  2. 2. |a| = 11.4
  3. 3. k = −22
  4. 4. a·b = 21
  5. 5. (a × b)z = 6
  6. 6. Mz = 150 N·m

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