The plane 2x – 3y + 6z – 11 = 0 makes an angle sin−1 (a) with x-axis. The value of ‘a’ is equal to:

$\frac{\sqrt{3}}{2}$ $\frac{\sqrt{2}}{3}$ $\frac{2}{7}$ $\frac{3}{7}$

$\frac{2}{7}$

If ' $\theta$ ' be the angle between the plane and x-axis, then $\sin \theta=\frac{2}{\sqrt{4+9+36}}=\frac{2}{7}$ $\Rightarrow \theta=\sin ^{-1}\left(\frac{2}{7}\right)$ $\Rightarrow a=\left(\frac{2}{7}\right)$