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:

Madison has fitted a triangular shade sail in her garden, as shown in the diagram.

Find the area of the shade sail. Give your answer correct to 2 decimal places.

  • A 25.30 m2
  • B 50.60 m2
  • C 50.30 m2
  • D 60.29 m2
  • E 96.45 m2

Q2:

A fly located at ( 2 , 4 , 7 ) is heading to an open jam jar located at ( 0 , − 2 , 1 0 ) . Given that it will reach the jam jar in 4 seconds, find the components of its velocity.

  • A ( 2 , 6 , − 3 )
  • B ( − 2 , − 6 , 3 )
  • C − 1 2 , 3 2 , − 3 4
  • D − 1 2 , − 3 2 , 3 4
  • E 1 2 , 3 2 , − 3 4

Q3:

If A and B are two nonzero vectors, and 𝜃 is the measure of the angle between them, find | × | + ( ⋅ ) A B A B .

  • A | | | | A B
  • B | | | | 𝜃 𝜃 A B s i n c o s
  • C0
  • D | | | | 𝜃 𝜃 A B s i n c o s
  • E1

Q4:

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

  • A 5 + 8 + 5 i j k
  • B − 5 − 8 − 5 i j k
  • C − 3 − 2 − 5 i j k
  • D 3 + 2 + 5 i j k

Q5:

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

  • A | 1 , 0 , 1 |
  • B | 0 , 0 , 1 |
  • C | 0 , 1 , 0 |
  • D | 1 , 1 , 1 |
  • E | 1 , 0 , 0 |

Q6:

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

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

Q7:

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

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

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