If a line has direction ratios proportional to 2, -1, -2, then what are its direction cosines?

Explanation

The direction cosines of a line are in the same ratio as that of the direction ratios, but the addition of their squares must yield 1 .


Thus, we find the direction cosines as under:


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`frac{2}{sqrt{4+1+4}}, frac{-1}{sqrt{4+1+4}}, frac{-2}{sqrt{4+1+4}}`< br>

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It can be verified that `frac{2^{2}+(-1)^{2}+(-2)^{2}}{4+1+4}=1`


Thus, the direction cosines are `frac{2}{3}, frac{-1}{3}, frac{-2}{3}`