Lesson Worksheet: Vectors in Space Mathematics • 12th Grade

In this worksheet, we will practice representing a vector in space using a three-dimensional coordinate system.


Find the unit vector in the direction of the 𝑦-axis.

  • A1,0,0
  • B0,0,1
  • C1,1,1
  • D1,0,1
  • E0,1,0


Which of the following is equal to the vector 𝐴𝐵?

  • A𝐴×𝐵
  • B𝐴+𝐵
  • C𝐴𝐵
  • D𝐵𝐴


Given A=6,1,4 and B=3,1,2, find 𝐴𝐵.

  • A18,1,8
  • B9,2,6
  • C3,0,2
  • D3,0,2
  • E9,2,6


Given 𝐴𝐵=1,3,0 and 𝑂𝐴=4,5,5, express 𝑂𝐵 in terms of the fundamental unit vectors.

  • A3+2+5ijk
  • B585ijk
  • C5+8+5ijk
  • D325ijk


Using the graph, find the vector 𝑂𝐴 in component form.

  • A5,0,0
  • B0,5,0
  • C0,5,0
  • D0,0,5
  • E5,0,0


Using the graph, Find the vector 𝑂𝐴 in the component form.

  • A0,1,0
  • B0,0,1
  • C1,0,0
  • D0,0,1
  • E0,1,0


Using the graph, write the vector A in terms of its components.

  • A4,3,2
  • B2,4,3
  • C3,2,4
  • D2,3,4


In the given figure, find vector 𝐴𝐵.

  • A6,0,0
  • B12,0,0
  • C0,0,6
  • D6,12,5
  • E6,0,0


Using the figure, express the vector 𝑂𝐶 in component form.

  • A3,5,0
  • B5,3,7
  • C4,6,0
  • D5,3,0
  • E5,3,0


Find the vector 𝐴𝐺 using the graph.

  • A3,3,2
  • B4,4,4
  • C1,3,3
  • D4,4,3
  • E3,3,3

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