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

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ConceptDirection Cosines and Direction Ratios of a Line

#### Question

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

#### Solution

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

$\text{ Now,}$

$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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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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