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Question
If a line has direction ratios proportional to 2, −1, −2, then what are its direction consines?
Solution
\[\text { If a line has direction ratios proportional to 2, - 1, and - 2, then its direction cosines are } \]
\[ \frac{2}{\sqrt{\left( 2 \right)^2 + \left( - 1 \right) + \left( - 2 \right)^2}}, \frac{- 1}{\sqrt{\left( 2 \right)^2 + \left( - 1 \right) + \left( - 2 \right)^2}}, \frac{- 2}{\sqrt{\left( 2 \right)^2 + \left( - 1 \right) + \left( - 2 \right)^2}} \]
\[ = \frac{2}{3}, - \frac{1}{3}, - \frac{2}{3}\]
\[\text { Thus, the direction cosines are } \frac{2}{3}, - \frac{1}{3}, - \frac{2}{3} .\]
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