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 = (−7, 7, −3).

a = (−7, 7, −3)
ûz =
2.Easy
xyza

Find the z-component ûz of the unit vector û that points in the direction of a = (−3, 6, −2).

a = (−3, 6, −2)
ûz =
3.Medium
xyzdFAB

A constant force F = (−5, −15, 20) N acts on an object while it moves in a straight line from point A(−1, 3, −4) to point B(4, 0, −2). Coordinates are in metres. Find the work W done by the force.

F = (−5, −15, 20) NA(−1, 3, −4) mB(4, 0, −2) m
W = J
4.Medium
xyzab

Find the dot product a·b of a = (3, 6, 6) and b = (−7, 4, 2).

a = (3, 6, 6)b = (−7, 4, 2)
a·b =
5.Hard
xyzABC

Find the area A of the triangle with corners A(−1, 3, 3), B(−4, −3, 2) and C(4, −2, 3). Coordinates are in metres.

A(−1, 3, 3)B(−4, −3, 2)C(4, −2, 3)
A = m²
6.Hard
xyzabc

Find the volume V of the parallelepiped whose edges from one corner are a = (3, −2, −5), b = (−3, 3, 3) and c = (−2, −1, −2).

a = (3, −2, −5)b = (−3, 3, 3)c = (−2, −1, −2)
V =

Answer key

  1. 1. ûz = −0.29
  2. 2. ûz = −0.2857
  3. 3. W = 60 J
  4. 4. a·b = 15
  5. 5. A = 22.78 m²
  6. 6. V = 30

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