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Reviewed CSCA Mathematics question · Standard

Given vectors u = (3, -2, 4) and v = (-1, 5, 2), what is the vector 2u - 3v?

  1. (9, -19, 2)
  2. (9, -19, 14)
  3. (9, 11, 2)
  4. (5, -19, 2)
Show the answer and explanation

Correct answer

A. (9, -19, 2)

Principle or equation

Vector addition and scalar multiplication are performed component-wise.

Why this answer is correct

2u = (6, -4, 8) and 3v = (-3, 15, 6). Then 2u - 3v = (6 - (-3), -4 - 15, 8 - 6) = (9, -19, 2).

Example

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

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