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 y-component ûy of the unit vector û that points in the direction of a = (0, 4, −2).

a = (0, 4, −2)
ûy =
2.Easy
xyza

Find the x-component ûx of the unit vector û that points in the direction of a = (4, −3, −6).

a = (4, −3, −6)
ûx =
3.Medium
xyzdFAB

A constant force F = (10, −25, 5) N acts on an object while it moves in a straight line from point A(−2, 0, 3) to point B(3, −5, 5). Coordinates are in metres. Find the work W done by the force.

F = (10, −25, 5) NA(−2, 0, 3) mB(3, −5, 5) m
W = J
4.Medium
xyzab

Find the angle θ between the vectors a = (−2, 0, −2) and b = (6, 5, −3), in degrees.

a = (−2, 0, −2)b = (6, 5, −3)
θ = °
5.Hard
xyzab

Find the area A of the parallelogram spanned by a = (4, −5, 6) and b = (−3, −3, 1).

a = (4, −5, 6)b = (−3, −3, 1)
A =
6.Hard
xyzab

The unit vector n̂ is perpendicular to both a = (4, −5, 2) and b = (−2, 4, 0) and has a positive z-component. Find its x-component n̂x.

a = (4, −5, 2)b = (−2, 4, 0)n̂z > 0
n̂x =

Answer key

  1. 1. ûy = 0.8944
  2. 2. ûx = 0.5121
  3. 3. W = 185 J
  4. 4. θ = 104.7 °
  5. 5. A = 37.18
  6. 6. n̂x = −0.7428

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