Share

Books Shortlist

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

ConceptDirection Cosines and Direction Ratios of a Line

#### 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?

#### Video TutorialsVIEW ALL [3]

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