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, −1, 2).

a = (−8, −1, 2)
|a| =
2.Easy
xy235°F = 270 N

A force of 270 N acts in the xy-plane at 235° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 270 Nθ = 235°
Fx = N
3.Medium
xyzab

Find the value of k for which the vectors a = (−5, 2, 3) and b = (0, 5, k) are perpendicular.

a = (−5, 2, 3)b = (0, 5, k)
k =
4.Medium
xyzab

Find the value of k for which the vectors a = (−1, 6, 4) and b = (−4, 2, k) are perpendicular.

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

For a = (−5, −5, 4) and b = (0, −5, −1), find the y-component (a × b)y of the cross product a × b.

a = (−5, −5, 4)b = (0, −5, −1)
(a × b)y =
6.Hard
xyzab

The unit vector n̂ is perpendicular to both a = (−3, 4, 3) and b = (−4, 1, 3) and has a positive z-component. Find its x-component n̂x.

a = (−3, 4, 3)b = (−4, 1, 3)n̂z > 0
n̂x =

Answer key

  1. 1. |a| = 8.307
  2. 2. Fx = −154.9 N
  3. 3. k = −3.333
  4. 4. k = −4
  5. 5. (a × b)y = −5
  6. 6. n̂x = 0.5592

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