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Reviewed CSCA Mathematics question · Hard

Given vectors u = (2, -1, 3) and v = (4, 2, -1), what is the vector 2u - 3v?

  1. (-8, -8, 9)
  2. (8, 8, -9)
  3. (-8, 8, -9)
  4. (8, -8, 9)
Show the answer and explanation

Correct answer

A. (-8, -8, 9)

Principle or equation

Vector scalar multiplication and subtraction are performed component-wise.

Why this answer is correct

2u = (4, -2, 6). 3v = (12, 6, -3). Then 2u - 3v = (4-12, -2-6, 6-(-3)) = (-8, -8, 9).

Example

If a = (1,2) and b = (3,4), then 2a - b = (2-3, 4-4) = (-1, 0).

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