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Question
If a line has direction ratios 2, −1, −2, determine its direction cosines.
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Solution
\[\text{Let the direction cosines of the line be l, m, n .} \]
\[\text{ Now,} \]
\[ l = \frac{2}{\sqrt{2^2 + \left( - 1 \right)^2 + \left( - 2 \right)^2}} = \frac{2}{3}\]\[m = \frac{- 1}{\sqrt{2^2 + \left( - 1 \right)^2 + \left( - 2 \right)^2}} = \frac{- 1}{3}\]\[n = \frac{- 2}{\sqrt{2^2 + \left( - 1 \right)^2 + \left( - 2 \right)^2}} = \frac{- 2}{3}\]\[\text{Therefore, the direction cosines of the line are }\frac{2}{3} , \frac{- 1}{3}, \frac{- 2}{3} .\]
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