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Question
If the direction ratios of a line are proportional to 1, −3, 2, then its direction cosines are
Options
\[\frac{1}{\sqrt{14}}, - \frac{3}{\sqrt{14}}, \frac{2}{\sqrt{14}}\]
\[\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}\]
\[- \frac{1}{\sqrt{14}}, \frac{3}{\sqrt{14}}, \frac{2}{\sqrt{14}}\]
\[- \frac{1}{\sqrt{14}}, - \frac{2}{\sqrt{14}}, - \frac{3}{\sqrt{14}}\]
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Solution
\[\frac{1}{\sqrt{14}}, - \frac{3}{\sqrt{14}}, \frac{2}{\sqrt{14}}\]
The direction ratios of the line are proportional to 1, -3, 2 .
∴ The direction cosines of the line are
\[\frac{1}{\sqrt{1^2 + \left( - 3 \right)^2 + 2^2}}, \frac{- 3}{\sqrt{1^2 + \left( - 3 \right)^2 + 2^2}}, \frac{2}{\sqrt{1^2 + \left( - 3 \right)^2 + 2^2}} \]
\[ = \frac{1}{\sqrt{14}}, \frac{- 3}{\sqrt{14}}, \frac{2}{\sqrt{14}}\]
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