Worksheet: Vectors in Space

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


A fly located at (2,4,7) is heading to an open jam jar located at (0,2,10). Given that it will reach the jam jar in 4 seconds, find the components of its velocity.

  • A(2,6,3)
  • B12,32,34
  • C12,32,34
  • D(2,6,3)
  • E12,32,34


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

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


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


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

  • A1,1,0
  • B1,1,1
  • C0,1,0
  • D1,0,0
  • E0,0,1


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

  • A0,1,1
  • B1,0,0
  • C0,0,1
  • D0,1,0
  • E1,1,1


Given A=𝑎,10,9 and B=3,𝑏,3, if 𝐴𝐵=5,3,𝑐, find the value of 𝑎+𝑏+𝑐.


Which of the following is equal to the vector 𝐴𝐵?

  • AAB×
  • BAB+
  • CAB
  • DBA


Find the vector 𝐴𝐺 using the graph.

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


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


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

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

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