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 = (−2, 8, −9).

a = (−2, 8, −9)
|a| =
2.Easy
xyza

Find the x-component ûx of the unit vector û that points in the direction of a = (4, 7, 7).

a = (4, 7, 7)
ûx =
3.Medium
xyzdFAB

A constant force F = (5, −15, −15) N acts on an object while it moves in a straight line from point A(4, −2, −3) to point B(0, −4, 1). Coordinates are in metres. Find the work W done by the force.

F = (5, −15, −15) NA(4, −2, −3) mB(0, −4, 1) m
W = J
4.Medium
xyzdFAB

A constant force F = (20, 25, 20) N acts on an object while it moves in a straight line from point A(−1, −4, −2) to point B(3, −3, 3). Coordinates are in metres. Find the work W done by the force.

F = (20, 25, 20) NA(−1, −4, −2) mB(3, −3, 3) m
W = J
5.Hard
xyzab

Find the area A of the parallelogram spanned by a = (−3, 5, 0) and b = (4, −6, 3).

a = (−3, 5, 0)b = (4, −6, 3)
A =
6.Hard
xyzab

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

a = (−1, −6, −5)b = (−3, −3, 3)
A =

Answer key

  1. 1. |a| = 12.21
  2. 2. ûx = 0.3746
  3. 3. W = −50 J
  4. 4. W = 205 J
  5. 5. A = 17.61
  6. 6. A = 40.47

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