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 = (2, −4, 2).

a = (2, −4, 2)
ûy =
2.Easy
xya

Find the magnitude |a| of the vector a = (6, 11).

a = (6, 11)
|a| =
3.Medium
xyzdFAB

A constant force F = (−15, −5, 0) N acts on an object while it moves in a straight line from point A(1, −1, 1) to point B(4, 4, −3). Coordinates are in metres. Find the work W done by the force.

F = (−15, −5, 0) NA(1, −1, 1) mB(4, 4, −3) m
W = J
4.Medium
xyzab

Find the angle θ between the vectors a = (1, 6, 5) and b = (6, −3, 4), in degrees.

a = (1, 6, 5)b = (6, −3, 4)
θ = °
5.Hard
xyzrFOA

A force F = (50, 10, −60) N acts at point A(2, 4, 0). Coordinates are in metres. Find the z-component Mz of the moment of the force about the origin O(0, 0, 0).

F = (50, 10, −60) NA(2, 4, 0) mO(0, 0, 0) m
Mz = N·m
6.Hard
xyzABC

Find the area A of the triangle with corners A(4, 4, 2), B(−3, −1, 1) and C(0, −3, −4). Coordinates are in metres.

A(4, 4, 2)B(−3, −1, 1)C(0, −3, −4)
A = m²

Answer key

  1. 1. ûy = −0.8165
  2. 2. |a| = 12.53
  3. 3. W = −70 J
  4. 4. θ = 82.53 °
  5. 5. Mz = −180 N·m
  6. 6. A = 26.52 m²

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