Worksheet: Vectors in Space

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

Q1:

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)
  • B−12,32,−34
  • C12,32,−34
  • D(2,6,−3)
  • E−12,−32,34

Q2:

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

  • A3+2+5ijk
  • B−5−8−5ijk
  • C5+8+5ijk
  • D−3−2−5ijk

Q3:

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

  • A⟨1,0,0⟩
  • B⟨0,0,1⟩
  • C⟨1,1,1⟩
  • D⟨1,0,1⟩
  • E⟨0,1,0⟩

Q4:

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

  • A⟨1,1,0⟩
  • B⟨1,1,1⟩
  • C⟨0,1,0⟩
  • D⟨1,0,0⟩
  • E⟨0,0,1⟩

Q5:

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

  • A⟨0,1,1⟩
  • B⟨1,0,0⟩
  • C⟨0,0,1⟩
  • D⟨0,1,0⟩
  • E⟨1,1,1⟩

Q6:

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

Q7:

Which of the following is equal to the vector 𝐴𝐵?

  • AAB×
  • BAB+
  • CAB−
  • DBA−

Q8:

Find the vector 𝐴𝐺 using the graph.

  • A⟨3,3,2⟩
  • B⟨4,4,4⟩
  • C⟨1,3,3⟩
  • D⟨4,4,3⟩
  • E⟨3,3,3⟩

Q9:

Given A=⟨6,1,4⟩ and B=⟨3,1,2⟩, find 𝐴𝐵.

  • A⟨18,1,8⟩
  • B⟨9,2,6⟩
  • C⟨3,0,2⟩
  • D⟨−3,0,−2⟩
  • E⟨−9,−2,−6⟩

Q10:

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

  • A⟨4,3,2⟩
  • B⟨2,4,3⟩
  • C⟨3,2,4⟩
  • D⟨2,3,4⟩

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