Discussion
If a straight line has direction ratios proportional to 2, -1, -2 then its direction cosines are
Answer: A
The direction cosines are \(\frac{2}{3}, -\frac{1}{3}, \frac{-2}{3}\).
Divide each direction ratio by the length of the vector (2, -1, -2):
\[ \sqrt{2^{2} + (-1)^{2} + (-2)^{2}} = \sqrt{9} = 3 \]
giving 2/3, -1/3, -2/3, whose squares add to 1. Dividing by 9 (the square of the length) gives option B, whose squares do not add to 1. Option C drops the minus signs, and option D changes the sign of only some terms, so it does not point along the same line.
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