What are the direction cosines of the vector ?

Answer and explanation

Correct answer: C.

  1. Step 1: Calculate magnitude: .
  2. Step 2: Divide each component by magnitude: .
  3. Step 3: Direction cosines are .
Answer
(\frac{2}{3}, -\frac{2}{3}, \frac{1}{3}).
Why not the others: '(\frac{2}{\sqrt{5}}, -\frac{2}{\sqrt{5}}, \frac{1}{\sqrt{5}})' ignores the -component in magnitude; '' are direction ratios, not direction cosines; '(\frac{4}{9}, \frac{4}{9}, \frac{1}{9})' squares the direction cosines.

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