Lesson Worksheet: Vectors in Space Mathematics • 12th Grade

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

Q1:

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⟩

Q2:

Which of the following is equal to the vector 𝐴𝐵?

  • A𝐴×𝐵
  • B𝐴+𝐵
  • C𝐴−𝐵
  • D𝐵−𝐴

Q3:

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⟩

Q4:

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

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

Q5:

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

  • A⟨5,0,0⟩
  • B⟨0,−5,0⟩
  • C⟨0,5,0⟩
  • D⟨0,0,5⟩
  • E⟨−5,0,0⟩

Q6:

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

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

Q7:

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⟩

Q8:

In the given figure, find vector 𝐴𝐵.

  • A⟨6,0,0⟩
  • B⟨−12,0,0⟩
  • C⟨0,0,−6⟩
  • D⟨−6,12,5⟩
  • E⟨−6,0,0⟩

Q9:

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

  • A⟨3,−5,0⟩
  • B⟨5,−3,7⟩
  • C⟨4,6,0⟩
  • D⟨5,3,0⟩
  • E⟨5,−3,0⟩

Q10:

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⟩

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