CSCAPrep
Reviewed CSCA Mathematics question · Standard

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

  1. (1, -14, 12)
  2. (1, -14, 0)
  3. (1, -10, 12)
  4. (7, -14, 12)
Show the answer and explanation

Correct answer

A. (1, -14, 12)

Principle or equation

Vector scalar multiplication and subtraction are performed component-wise.

Why this answer is correct

2u = (4, -2, 6). 3v = (3, 12, -6). 2u - 3v = (4-3, -2-12, 6-(-6)) = (1, -14, 12).

Example

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

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