Question

The plane $2x-3y+6z-11=0$ makes an angle ${\sin }^{-1}\alpha$ with X-axis. The value of $\alpha$ is equal to

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{\sqrt{2}}{3}$
• C. $\frac{2}{7}$
• D. $\frac{3}{7}$

Answer 1

The correct option is C $\frac{2}{7}$

$\frac{\pi }{2}-\theta ={\cos }^{-1}\frac{2}{\sqrt{2^2+3^2+6^2}}\frac{\pi }{2}-\theta ={\cos }^{-1}\frac{2}{7}\theta ={\sin }^{-1}\frac{2}{7}$