CBSE (Arts) Class 12CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Write the Inclination of a Line with Z-axis, If Its Direction Ratios Are Proportional to 0, 1, −1. - CBSE (Arts) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

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

Solution

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

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

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

\[\text{ Now }, \]

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

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

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

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

 

  Is there an error in this question or solution?

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: 11 | Page no. 25
Solution Write the Inclination of a Line with Z-axis, If Its Direction Ratios Are Proportional to 0, 1, −1. Concept: Direction Cosines and Direction Ratios of a Line.
S
View in app×