If the plane $2x - 3y + 6z - 11 = 0$ makes an angle ${\sin ^{ - 1}}\alpha$ with $X$-axis, then the value of $\alpha$ is

Since, $2x - 3y + 6z - 11 = 0$ makes an angle ${\sin ^{ - 1}}\alpha$ with X-axis.

$\overrightarrow {\rm{b}} = (1\widehat {\rm{i}} + 0\widehat {\rm{j}} + 0\widehat {\rm{k}})$

and $\overrightarrow {\rm{n}} = 2\widehat {\rm{i}} - 3\widehat {\rm{j}} + 6\widehat {\rm{k}}$

As we know, $\sin \theta = \frac{{|\overrightarrow {\rm{b}} \cdot \overrightarrow {\rm{n}} |}}{{|\overrightarrow {\rm{b}} | \cdot |\overrightarrow {\rm{n}} |}}$

$= \frac{{|(1\widehat {\rm{i}}) \cdot (2\widehat {\rm{i}} - 3\widehat {\rm{j}} + 6\widehat {\rm{k}})|}}{{\sqrt 1 \sqrt {4 + 9 + 36} }} = \frac{2}{7}$