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

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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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APPEARS IN

 RD Sharma Solution for Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) (2018 to Current)
Chapter 27: Direction Cosines and Direction Ratios
Ex.Very Short Answers | Q: 17 | Page no. 25
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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