Worksheet: Operations on Vectors in Space

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In this worksheet, we will practice how to make operations on vectors in space, such as vector addition, vector subtraction, and scalar multiplication.

Q1:

Given that A B + = ⟨ − 2 , 4 , 3 ⟩ and A = ⟨ 3 , 5 , 3 ⟩ , determine | | B .

  • A √ 1 1 8
  • B26
  • C118
  • D √ 2 6

Q2:

Find the value of ‖ ‖ ⃑ 𝐴 × ⃑ 𝐵 ‖ ‖ + | ⃑ 𝐴 ⋅ ⃑ 𝐵 | 2 ‖ ‖ ⃑ 𝐴 ‖ ‖ ‖ ‖ ⃑ 𝐵 ‖ ‖ 2 2 2 2 .

  • A2
  • B1
  • C0
  • D 1 2
  • E 1 4

Q3:

Suppose ⃑ 𝐴 and ⃑ 𝐵 are two vectors in ℝ 3 . Is ‖ ‖ ⃑ 𝐴 + ⃑ 𝐵 ‖ ‖ = ‖ ‖ ⃑ 𝐴 ‖ ‖ + ‖ ‖ ⃑ 𝐵 ‖ ‖ ? If not, which is greater?

  • Ayes
  • Bno, ‖ ‖ ⃑ 𝐴 + ⃑ 𝐵 ‖ ‖
  • Cno, ‖ ‖ ⃑ 𝐴 ‖ ‖ + ‖ ‖ ⃑ 𝐵 ‖ ‖

Q4:

If A i j k = − 5 − 8 + 6 and B i j k = 4 − 3 + 1 3 , find A B − .

  • A − 9 − 1 1 − 2 0 i j k
  • B − − 1 1 + 1 9 i j k
  • C − 1 1 − 4 − 2 0 i j k
  • D − 9 − 5 − 7 i j k

Q5:

If A = ⟨ − 8 , 9 , 9 ⟩ and B = ⟨ − 6 , 4 , 9 ⟩ , find 2 5 − 4 5 A B .

  • A − 8 , 2 5 , − 1 8 5
  • B 8 , 2 5 , − 1 8 5
  • C 8 5 , 2 5 , − 1 8 5

Q6:

If A = ⟨ − 1 , 1 , 1 ⟩ , and B = ⟨ 1 , 1 , − 2 ⟩ , determine the vector C for which 2 + 5 = 5 C A B .

  • A 0 , 5 , − 5 2
  • B ⟨ 1 0 , 0 , − 1 5 ⟩
  • C 3 , 2 , − 1 1 2
  • D 5 , 0 , − 1 5 2

Q7:

and are two vectors, where and . Comparing and , which quantity is larger?

  • AThey are both the same.
  • B
  • C

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