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Reviewed CSCA Mathematics question · Easy

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

  1. (8, -17)
  2. (4, -1)
  3. (8, -1)
  4. (4, -17)
Show the answer and explanation

Correct answer

A. (8, -17)

Principle or equation

Scalar multiplication multiplies each component; vector addition/subtraction combines corresponding components.

Why this answer is correct

3u = (6, -9); 2v = (-2, 8); 3u - 2v = (6 - (-2), -9 - 8) = (8, -17).

Example

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

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