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)
$\cos \theta =\left(\frac{2.0+\left(-1\right).0+\left(2\right)\left(1\right)}{\sqrt{2^2+1^2+2^2}\sqrt{0^2+0^2+1}}\right)=\frac{2}{3}$
$\Rightarrow \theta$ = ${\cos }^{-1}\left(\frac{2}{3}\right)$