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
xy30°F = 210 N

A force of 210 N acts in the xy-plane at 30° measured anticlockwise from the positive x-axis. Find its x-component Fx.

F = 210 Nθ = 30°
Fx = N
2.Easy
xyza

Find the magnitude |a| of the vector a = (7, 6, 4).

a = (7, 6, 4)
|a| =
3.Medium
xyzab

Find the scalar projection compb a of a = (−6, 3, −2) onto b = (4, 3, −1), that is, the component of a in the direction of b.

a = (−6, 3, −2)b = (4, 3, −1)
compb a =
4.Medium
xyzab

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

a = (2, −5, −6)b = (−6, 6, 3)
a·b =
5.Hard
xyzab

For a = (−3, −2, −4) and b = (5, 2, −6), find the x-component (a × b)x of the cross product a × b.

a = (−3, −2, −4)b = (5, 2, −6)
(a × b)x =
6.Hard
xyzab

The unit vector n̂ is perpendicular to both a = (3, −2, 5) and b = (−5, 4, −4) and has a positive z-component. Find its y-component n̂y.

a = (3, −2, 5)b = (−5, 4, −4)n̂z > 0
n̂y =

Answer key

  1. 1. Fx = 181.9 N
  2. 2. |a| = 10.05
  3. 3. compb a = −2.55
  4. 4. a·b = −60
  5. 5. (a × b)x = 20
  6. 6. n̂y = −0.7302

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