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 = (−8, −8, 7).

a = (−8, −8, 7)
ûx =
2.Easy
xyza

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

a = (−4, −4, 3)
ûy =
3.Medium
xyzab

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

a = (−6, −2, 6)b = (−4, 2, k)
k =
4.Medium
xyzab

Find the scalar projection compb a of a = (−7, −3, −2) onto b = (3, −4, 1), that is, the component of a in the direction of b.

a = (−7, −3, −2)b = (3, −4, 1)
compb a =
5.Hard
xyzrFOA

A force F = (10, 50, 10) N acts at point A(3, −2, 0). Coordinates are in metres. Find the z-component Mz of the moment of the force about point O(−3, 0, −3).

F = (10, 50, 10) NA(3, −2, 0) mO(−3, 0, −3) m
Mz = N·m
6.Hard
xyzab

The unit vector n̂ is perpendicular to both a = (−2, −4, −1) and b = (−4, −4, 0) and has a positive z-component. Find its y-component n̂y.

a = (−2, −4, −1)b = (−4, −4, 0)n̂z > 0
n̂y =

Answer key

  1. 1. ûx = −0.6013
  2. 2. ûy = −0.6247
  3. 3. k = −3.333
  4. 4. compb a = −2.157
  5. 5. Mz = 320 N·m
  6. 6. n̂y = −0.4082

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