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 x-component ûx of the unit vector û that points in the direction of a = (5, −5, −1).

a = (5, −5, −1)
ûx =
2.Easy
xyza

Find the z-component ûz of the unit vector û that points in the direction of a = (7, 6, −6).

a = (7, 6, −6)
ûz =
3.Medium
xyzab

Find the dot product a·b of a = (5, −3, 4) and b = (1, −3, 2).

a = (5, −3, 4)b = (1, −3, 2)
a·b =
4.Medium
xyzdFAB

A constant force F = (25, 30, −10) N acts on an object while it moves in a straight line from point A(2, 1, −5) to point B(−2, −4, 0). Coordinates are in metres. Find the work W done by the force.

F = (25, 30, −10) NA(2, 1, −5) mB(−2, −4, 0) m
W = J
5.Hard
xyzab

The unit vector n̂ is perpendicular to both a = (4, 2, −5) and b = (−4, 3, −3) and has a positive z-component. Find its y-component n̂y.

a = (4, 2, −5)b = (−4, 3, −3)n̂z > 0
n̂y =
6.Hard
xyzab

For a = (−5, −4, 5) and b = (−2, 1, −5), find the x-component (a × b)x of the cross product a × b.

a = (−5, −4, 5)b = (−2, 1, −5)
(a × b)x =

Answer key

  1. 1. ûx = 0.7001
  2. 2. ûz = −0.5455
  3. 3. a·b = 22
  4. 4. W = −300 J
  5. 5. n̂y = 0.8249
  6. 6. (a × b)x = 15

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