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
xy75°F = 130 N

A force of 130 N acts in the xy-plane at 75° measured anticlockwise from the positive x-axis. Find its y-component Fy.

F = 130 Nθ = 75°
Fy = N
2.Easy
xyza

Find the y-component ûy of the unit vector û that points in the direction of a = (−3, 4, 6).

a = (−3, 4, 6)
ûy =
3.Medium
xyzdFAB

A constant force F = (−25, −20, −30) N acts on an object while it moves in a straight line from point A(1, −4, −2) to point B(0, −4, −4). Coordinates are in metres. Find the work W done by the force.

F = (−25, −20, −30) NA(1, −4, −2) mB(0, −4, −4) m
W = J
4.Medium
xyzab

Find the scalar projection compb a of a = (−1, −7, 5) onto b = (−4, 3, −5), that is, the component of a in the direction of b.

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

A force F = (40, −20, −30) N acts at point A(−1, 3, −4). Coordinates are in metres. Find the magnitude |M| of the moment of the force about point O(3, 0, 3).

F = (40, −20, −30) NA(−1, 3, −4) mO(3, 0, 3) m
|M| = N·m
6.Hard
xyzab

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

a = (−3, −6, −5)b = (1, −3, −3)
A =

Answer key

  1. 1. Fy = 125.6 N
  2. 2. ûy = 0.5121
  3. 3. W = 85 J
  4. 4. compb a = −5.94
  5. 5. |M| = 463.1 N·m
  6. 6. A = 20.74

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