Q101 / 160 · TS EAMCET 2023 (12 May Shift 2) · Mathematics
A line $L$ is parallel to both the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$. If line $L$ makes an angle $\alpha$ with the positive direction of X-axis, then $\cos \alpha=$
- Correct answerA$\frac{1}{\sqrt{3}}$
- B$\frac{1}{\sqrt{2}}$
- C$\frac{1}{2}$
- D$\frac{\sqrt{3}}{2}$
Solution
Line parallel to both planes will be perpendicular to Angle with $X$ axis $=\alpha$
$$
\begin{aligned}
& \therefore \quad \cos \alpha=\frac{3}{\sqrt{3^2+(-3)^2+3^2}}=\frac{3}{3 \sqrt{3}} \\
& \therefore \quad \cos \alpha=\frac{1}{\sqrt{3}} .
\end{aligned}
$$
Hence, the correct answer is option: 'A'.