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
xyza

Find the z-component ûz of the unit vector û that points in the direction of a = (−4, 5, −3).

a = (−4, 5, −3)
ûz =
2.Easy
xy325°F = 320 N

A force of 320 N acts in the xy-plane at 325° measured anticlockwise from the positive x-axis. Find its y-component Fy.

F = 320 Nθ = 325°
Fy = N
3.Medium
xyzab

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

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

Find the scalar projection compb a of a = (5, −4, −7) onto b = (5, 3, 0), that is, the component of a in the direction of b.

a = (5, −4, −7)b = (5, 3, 0)
compb a =
5.Hard
xyzabc

Find the volume V of the parallelepiped whose edges from one corner are a = (4, 3, 0), b = (3, 1, −3) and c = (−3, −3, −3).

a = (4, 3, 0)b = (3, 1, −3)c = (−3, −3, −3)
V =
6.Hard
xyzab

For a = (1, 1, 2) and b = (2, −3, 2), find the y-component (a × b)y of the cross product a × b.

a = (1, 1, 2)b = (2, −3, 2)
(a × b)y =

Answer key

  1. 1. ûz = −0.4243
  2. 2. Fy = −183.5 N
  3. 3. k = −0.3333
  4. 4. compb a = 2.229
  5. 5. V = 6
  6. 6. (a × b)y = 2

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