# the plane 2x-3y+6z=11 makes and angle arcsin alpha with x axis the value of alpha is

The angle $\alpha$ made by the plane and the line is  given by

$sin\alpha =\large\frac{\overrightarrow b.\overrightarrow n}{|\overrightarrow b||\overrightarrow n|}$

where $\overrightarrow b = 2\hat i-3\hat j+6\hat k\:\: and\:\:\overrightarrow b = i$

$\therefore\: sin\alpha =\large\frac{ (2\hat i-3\hat j+6\hat k).(\hat i)}{\sqrt {2^2+(-3)^2+(6)^2} .\sqrt 1^2}$
$=\large\frac{2}{7}$

$\therefore \:\alpha = sin^{-1}\large\frac{2}{7}$
edited Oct 24, 2013