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, −7, −5).

a = (4, −7, −5)
ûz =
2.Easy
xyza

Find the z-component ûz of the unit vector û that points in the direction of a = (−8, 0, 3).

a = (−8, 0, 3)
ûz =
3.Medium
xyzdFAB

A constant force F = (−30, −10, −10) N acts on an object while it moves in a straight line from point A(−2, −5, 1) to point B(4, −4, −3). Coordinates are in metres. Find the work W done by the force.

F = (−30, −10, −10) NA(−2, −5, 1) mB(4, −4, −3) m
W = J
4.Medium
xyzab

Find the angle θ between the vectors a = (−2, −6, 4) and b = (−6, −5, 4), in degrees.

a = (−2, −6, 4)b = (−6, −5, 4)
θ = °
5.Hard
xyzab

The unit vector n̂ is perpendicular to both a = (−3, 2, −2) and b = (2, 1, 5) and has a positive z-component. Find its y-component n̂y.

a = (−3, 2, −2)b = (2, 1, 5)n̂z > 0
n̂y =
6.Hard
xyzab

The unit vector n̂ is perpendicular to both a = (4, −5, 1) and b = (3, 5, 1) and has a positive z-component. Find its y-component n̂y.

a = (4, −5, 1)b = (3, 5, 1)n̂z > 0
n̂y =

Answer key

  1. 1. ûz = −0.527
  2. 2. ûz = 0.3511
  3. 3. W = −150 J
  4. 4. θ = 27.96 °
  5. 5. n̂y = −0.6208
  6. 6. n̂y = −0.02746

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