Let $L$ be the line of intersection of the planes $2x + 3y + \mathcal{z} = 1$ and $x + 3y + 2\mathcal{z} = 2$. If $L$ makes an angle $\alpha$ with the positive $x$-axis, then $\cos\alpha$ equals

Question

Dr. Abubacker · Accepted Answer

(d)
Since line of intersection is perpendicular to both the planes, direction ratios of the line of intersection
$= \left| \begin{matrix}
\widehat{i} & \widehat{j} & \widehat{k} \
2 & 3 & 1 \
1 & 3 & 2
\end{matrix} ight| = 3\widehat{i} - 3\widehat{j} + 3\widehat{k}$
Hence, $\cos\alpha = \frac{3}{\sqrt{9 + 9 + 9}} = \frac{1}{\sqrt{3}}$

Q. Let $L$ be the line of intersection of the planes $2x + 3y + \mathcal{z} = 1$ and $x + 3y + 2\mathcal{z} = 2$. If $L$ makes an angle $\alpha$ with the positive $x$-axis, then $\cos\alpha$ equals

Explanation

Reviewed by Dr. Abubacker

Want more practice?