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# Solution for If a Line Has Direction Ratios Proportional to 2, −1, −2, Then What Are Its Direction Consines? - CBSE (Commerce) Class 12 - Mathematics

ConceptDirection Cosines and Direction Ratios of a Line

#### 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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Solution If a Line Has Direction Ratios Proportional to 2, −1, −2, Then What Are Its Direction Consines? Concept: Direction Cosines and Direction Ratios of a Line.
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