Search any question & find its solution
Question:
Answered & Verified by Expert
If a line has the direction ratios $-18,12,-4$ then what are its direction cosines?
Solution:
1846 Upvotes
Verified Answer
Now given direction ratios of a line are $-8,12,-4$ $\therefore \quad \mathrm{a}=-18, \mathrm{~b}=12, \mathrm{c}=-4$
Direction cosines are
$$
\begin{aligned}
&l=\frac{a}{\sqrt{a^2+b^2+c^2}}=\frac{-9}{11}, \quad m=\frac{b}{\sqrt{a^2+b^2+c^2}}=\frac{6}{11} \\
&n=\frac{c}{\sqrt{a^2+b^2+c^2}}=\frac{-2}{11}
\end{aligned}
$$
Hence, direction cosines are $\frac{-9}{11}, \frac{6}{11}, \frac{-2}{11}$
Direction cosines are
$$
\begin{aligned}
&l=\frac{a}{\sqrt{a^2+b^2+c^2}}=\frac{-9}{11}, \quad m=\frac{b}{\sqrt{a^2+b^2+c^2}}=\frac{6}{11} \\
&n=\frac{c}{\sqrt{a^2+b^2+c^2}}=\frac{-2}{11}
\end{aligned}
$$
Hence, direction cosines are $\frac{-9}{11}, \frac{6}{11}, \frac{-2}{11}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.