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Reviewed CSCA Mathematics question · Easy

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

  1. (5, -11, 12)
  2. (5, 11, 12)
  3. (13, 5, 0)
  4. (5, -11, 0)
Show the answer and explanation

Correct answer

A. (5, -11, 12)

Principle or equation

Vector scalar multiplication multiplies each component, and vector subtraction subtracts corresponding components.

Why this answer is correct

Compute 3u = (9, -3, 6) and 2v = (4, 8, -6). Then 3u - 2v = (9-4, -3-8, 6-(-6)) = (5, -11, 12).

Example

If u = (1, 2) and v = (3, 4), then 2u - v = (2-3, 4-4) = (-1, 0).

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