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

Find the magnitude |a| of the vector a = (−6, 3, −3).

a = (−6, 3, −3)

|a| =

2.Easy

Find the magnitude |a| of the vector a = (6, 3, −1).

a = (6, 3, −1)

|a| =

3.Medium

Find the scalar projection comp_b a of a = (−3, −6, −6) onto b = (1, −3, −5), that is, the component of a in the direction of b.

a = (−3, −6, −6)b = (1, −3, −5)

comp_b a =

4.Medium

A constant force F = (15, 15, 5) N acts on an object while it moves in a straight line from point A(0, −1, −5) to point B(3, 4, 2). Coordinates are in metres. Find the work W done by the force.

F = (15, 15, 5) NA(0, −1, −5) mB(3, 4, 2) m

W = J

5.Hard

A force F = (10, −40, −20) N acts at point A(−1, 4, 1). Coordinates are in metres. Find the x-component M_x of the moment of the force about the origin O(0, 0, 0).

F = (10, −40, −20) NA(−1, 4, 1) mO(0, 0, 0) m

M_x = N·m

6.Hard

A force F = (50, −60, 0) N acts at point A(4, 1, 4). Coordinates are in metres. Find the x-component M_x of the moment of the force about the origin O(0, 0, 0).

F = (50, −60, 0) NA(4, 1, 4) mO(0, 0, 0) m

M_x = N·m

Answer key

1. |a| = 7.348
2. |a| = 6.782
3. comp_b a = 7.606
4. W = 155 J
5. M_x = −40 N·m
6. M_x = 240 N·m

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