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

Two forces act at a point in the xy-plane: F₁ = 120 N at 5° and F₂ = 20 N at 155°, both measured anticlockwise from the positive x-axis. Find the direction φ of their resultant, measured anticlockwise from the positive x-axis (between 0° and 360°).

F₁ = 120 N, θ₁ = 5°F₂ = 20 N, θ₂ = 155°

φ = °

2.Easy

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

a = (4, 4, 4)

û_y =

3.Medium

Find the scalar projection comp_b a of a = (6, −4, −6) onto b = (1, −3, −5), that is, the component of a in the direction of b.

a = (6, −4, −6)b = (1, −3, −5)

comp_b a =

4.Medium

Find the value of k for which the vectors a = (4, 1, −4) and b = (6, −2, k) are perpendicular.

a = (4, 1, −4)b = (6, −2, k)

k =

5.Hard

Find the volume V of the parallelepiped whose edges from one corner are a = (1, −2, −1), b = (−5, 4, −5) and c = (0, 4, 1).

a = (1, −2, −1)b = (−5, 4, −5)c = (0, 4, 1)

V =

6.Hard

For a = (−4, −3, 1) and b = (−6, 0, −1), find the x-component (a × b)_x of the cross product a × b.

a = (−4, −3, 1)b = (−6, 0, −1)

(a × b)_x =

Answer key

1. φ = 10.56 °
2. û_y = 0.5774
3. comp_b a = 8.113
4. k = 5.5
5. V = 34
6. (a × b)_x = 3

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