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Worksheet: Operations on Vectors in Space

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

Q1:

V and W are two vectors, where V = ⟨ − 1 , 5 , − 2 ⟩ and W = ⟨ 3 , 1 , 1 ⟩ . Comparing | − | V W and | | − | | V W , which quantity is larger?

  • AThey are both the same.
  • B | | − | | V W
  • C | − | V W

Q2:

If and , find .

  • A
  • B
  • C
  • D

Q3:

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

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

Q4:

If and , find .

  • A
  • B
  • C

Q5:

Find the value of .

  • A2
  • B1
  • C0
  • D
  • E

Q6:

Suppose and are two vectors in . Is ? If not, which is greater?

  • Ayes
  • Bno,
  • Cno,

Q7:

If , and , determine the vector for which .

  • A
  • B
  • C
  • D

Q8:

Given that the coordinates of and are and , respectively, determine .

  • A
  • B7
  • C
  • D

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