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
xy245°F = 140 N

A force of 140 N acts in the xy-plane at 245° measured anticlockwise from the positive x-axis. Find its y-component Fy.

F = 140 Nθ = 245°
Fy = N
2.Easy
xy60°F = 470 N

A force of 470 N acts in the xy-plane at 60° measured anticlockwise from the positive x-axis. Find its y-component Fy.

F = 470 Nθ = 60°
Fy = N
3.Medium
xyzdFAB

A constant force F = (−25, −15, −30) N acts on an object while it moves in a straight line from point A(2, 0, 5) to point B(−3, 2, 0). Coordinates are in metres. Find the work W done by the force.

F = (−25, −15, −30) NA(2, 0, 5) mB(−3, 2, 0) m
W = J
4.Medium
xyzab

Find the dot product a·b of a = (0, −5, −1) and b = (−2, −3, −2).

a = (0, −5, −1)b = (−2, −3, −2)
a·b =
5.Hard
xyzrFOA

A force F = (30, 10, 20) N acts at point A(−3, 2, 1). Coordinates are in metres. Find the x-component Mx of the moment of the force about point O(0, −1, 1).

F = (30, 10, 20) NA(−3, 2, 1) mO(0, −1, 1) m
Mx = N·m
6.Hard
xyzab

The unit vector n̂ is perpendicular to both a = (−5, 5, −2) and b = (0, −3, 1) and has a positive z-component. Find its y-component n̂y.

a = (−5, 5, −2)b = (0, −3, 1)n̂z > 0
n̂y =

Answer key

  1. 1. Fy = −126.9 N
  2. 2. Fy = 407 N
  3. 3. W = 245 J
  4. 4. a·b = 17
  5. 5. Mx = 60 N·m
  6. 6. n̂y = 0.3156

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