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Solution for If a Line Has Direction Ratios 2, −1, −2, Determine Its Direction Cosines. - CBSE (Commerce) Class 12 - Mathematics

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Question

If a line has direction ratios 2, −1, −2, determine its direction cosines.

Solution

 

\[\text{Let the direction cosines of the line be l, m, n .} \]

\[Now, \]

\[ l = \frac{2}{\sqrt{2^2 + \left( - 1 \right)^2 + \left( - 2 \right)^2}} = \frac{2}{3}\]\[m = \frac{- 1}{\sqrt{2^2 + \left( - 1 \right)^2 + \left( - 2 \right)^2}} = \frac{- 1}{3}\]\[n = \frac{- 2}{\sqrt{2^2 + \left( - 1 \right)^2 + \left( - 2 \right)^2}} = \frac{- 2}{3}\]\[\text{Therefore, the direction cosines of the line are }\frac{2}{3} , \frac{- 1}{3}, \frac{- 2}{3} .\]

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Solution If a Line Has Direction Ratios 2, −1, −2, Determine Its Direction Cosines. Concept: Direction Cosines and Direction Ratios of a Line.
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