Search any question & find its solution
Question:
Answered & Verified by Expert
Let $L$ be the line of intersection of the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$. If $L$ makes an angles $\alpha$ with the positive $x$-axis, then $\cos \alpha$ equals
Options:
Solution:
1342 Upvotes
Verified Answer
The correct answer is:
$\frac{1}{\sqrt{3}}$
$\frac{1}{\sqrt{3}}$
If direction cosines of $L$ be $l$, $m, n$, then
$\begin{aligned}
& 2 l+3 m+n=0 \\
& l+3 m+2 n=0
\end{aligned}$
Solving, we get, $\frac{l}{3}=\frac{m}{-3}=\frac{n}{3}$
$\therefore l: m: n=\frac{1}{\sqrt{3}}:-\frac{1}{\sqrt{3}}: \frac{1}{\sqrt{3}} \Rightarrow \cos \alpha=\frac{1}{\sqrt{3}} \text {. }$
$\begin{aligned}
& 2 l+3 m+n=0 \\
& l+3 m+2 n=0
\end{aligned}$
Solving, we get, $\frac{l}{3}=\frac{m}{-3}=\frac{n}{3}$
$\therefore l: m: n=\frac{1}{\sqrt{3}}:-\frac{1}{\sqrt{3}}: \frac{1}{\sqrt{3}} \Rightarrow \cos \alpha=\frac{1}{\sqrt{3}} \text {. }$
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.