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Write the Inclination of a Line with Z-axis, If Its Direction Ratios Are Proportional to 0, 1, −1.

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Question

Write the inclination of a line with Z-axis, if its direction ratios are proportional to 0, 1, −1.

Sum
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Solution

\[ \text{ We know that if a line has direction ratio } \left( a, b, c \right), \text{ then the cosine of its angle with the z - axis is given } by\]

\[\cos \gamma = \frac{c}{\sqrt{a^2 + b^2 + c^2}}\]

\[\text { Suppose the inclination of the line with direction ratio } \left( 0, 1, - 1 \right) \text{ with z - axis is } \gamma . \]

\[\text{ Now }, \]

\[\cos \lambda = \frac{- 1}{\sqrt{0 + 1 + 1}}\]

\[ = - \frac{1}{\sqrt{2}} \]

\[ \Rightarrow \lambda = \frac{3\pi}{4}\]

\[\text{ Hence, the inclination of the line with z - axis is } \frac{3\pi}{4} . \]

 

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Chapter 26: Direction Cosines and Direction Ratios - Very Short Answers [Page 25]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 26 Direction Cosines and Direction Ratios
Very Short Answers | Q 11 | Page 25

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