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
xy110°20°F1​F2​

Two forces act at a point in the xy-plane: F₁ = 250 N at 110° and F₂ = 230 N at 20°, both measured anticlockwise from the positive x-axis. Find the magnitude R of their resultant.

F1 = 250 N, θ1 = 110°F2 = 230 N, θ2 = 20°
R = N
2.Easy
xy55°F = 460 N

A force of 460 N acts in the xy-plane at 55° measured anticlockwise from the positive x-axis. Find its y-component Fy.

F = 460 Nθ = 55°
Fy = N
3.Medium
xyzab

Find the dot product a·b of a = (−3, −7, −6) and b = (−1, 0, 5).

a = (−3, −7, −6)b = (−1, 0, 5)
a·b =
4.Medium
xyzab

Find the dot product a·b of a = (−1, −6, 3) and b = (3, 6, −5).

a = (−1, −6, 3)b = (3, 6, −5)
a·b =
5.Hard
xyzrFOA

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

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

A force F = (−40, 10, 20) N acts at point A(2, −1, 1). Coordinates are in metres. Find the x-component Mx of the moment of the force about point O(3, 3, 3).

F = (−40, 10, 20) NA(2, −1, 1) mO(3, 3, 3) m
Mx = N·m

Answer key

  1. 1. R = 339.7 N
  2. 2. Fy = 376.8 N
  3. 3. a·b = −27
  4. 4. a·b = −54
  5. 5. My = 60 N·m
  6. 6. Mx = −60 N·m

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