Question

The angle between a normal to the plane $2x - y + 2z - 1 = 0$ and the z-axis is

• A. $\cos^{-1}\left(\frac{1}{3}\right)$
• B. $\sin^{-1}\left(\frac{2}{3}\right)$
• C. $\cos^{-1}\left(\frac{2}{3}\right)$
• D. $\sin^{-1}\left(\frac{1}{5}\right)$

Answer 1

Answer: (C)

d.r.s of the normal is (2, -1, 2)
d.r.s of z-axis is (0, 0, 1)
$\cos \theta = \left(\frac{2.0 + \left(-1\right).0 + \left(2\right)\left(1\right)}{\sqrt{2^{2} + 1^{2} +2^{2}} \sqrt{0^{2} + 0^{2} +1}}\right) = \frac{2}{3}$
$ \Rightarrow \, \, \, \theta$ = $\cos^{-1} \left(\frac{2}{3}\right)$