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 y-component ûy of the unit vector û that points in the direction of a = (8, −7, 2).

a = (8, −7, 2)
ûy =
2.Easy
xya

Find the magnitude |a| of the vector a = (−7, −2).

a = (−7, −2)
|a| =
3.Medium
xyzab

Find the value of k for which the vectors a = (−6, −4, 6) and b = (5, k, −1) are perpendicular.

a = (−6, −4, 6)b = (5, k, −1)
k =
4.Medium
xyzab

Find the angle θ between the vectors a = (−1, −3, −6) and b = (0, −2, 2), in degrees.

a = (−1, −3, −6)b = (0, −2, 2)
θ = °
5.Hard
xyzABC

Find the area A of the triangle with corners A(−3, 4, 2), B(−1, 3, 0) and C(−2, −2, −2). Coordinates are in metres.

A(−3, 4, 2)B(−1, 3, 0)C(−2, −2, −2)
A = m²
6.Hard
xyzABC

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

A(2, 4, −4)B(−2, −4, 2)C(−2, −3, 2)
A = m²

Answer key

  1. 1. ûy = −0.6472
  2. 2. |a| = 7.28
  3. 3. k = −9
  4. 4. θ = 108.2 °
  5. 5. A = 7.433 m²
  6. 6. A = 3.606 m²

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