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

A force of 40 N acts in the xy-plane at 85° measured anticlockwise from the positive x-axis. Find its y-component F_y.

F = 40 Nθ = 85°

F_y = N

2.Easy

Find the magnitude |a| of the vector a = (3, 0, 8).

a = (3, 0, 8)

|a| =

3.Medium

Find the dot product a·b of a = (0, −6, −5) and b = (−2, 5, −3).

a = (0, −6, −5)b = (−2, 5, −3)

a·b =

4.Medium

Find the scalar projection comp_b a of a = (−2, −1, 5) onto b = (2, 5, 4), that is, the component of a in the direction of b.

a = (−2, −1, 5)b = (2, 5, 4)

comp_b a =

5.Hard

A force F = (60, −40, 50) N acts at point A(−2, −2, −1). Coordinates are in metres. Find the x-component M_x of the moment of the force about point O(−1, 2, 3).

F = (60, −40, 50) NA(−2, −2, −1) mO(−1, 2, 3) m

M_x = N·m

6.Hard

For a = (1, −4, −1) and b = (−2, 6, −2), find the y-component (a × b)_y of the cross product a × b.

a = (1, −4, −1)b = (−2, 6, −2)

(a × b)_y =

Answer key

1. F_y = 39.85 N
2. |a| = 8.544
3. a·b = −15
4. comp_b a = 1.64
5. M_x = −360 N·m
6. (a × b)_y = 4

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