Question

The angle between the line $\frac{x-1}{1}=\frac{y+2}{1}=\frac{z-4}{0}$ and the plane $y+z+2=0$ is

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is C $\frac{\pi }{6}$

$\sin \theta =\frac{1\cdot 0+1\cdot 1+0\cdot 1}{\left(\sqrt{1^2+1^2+0^2}\right)\cdot \left(\sqrt{0^2+1^2+1^2}\right)}\sin \theta =\frac{1}{\sqrt{2}\cdot \sqrt{2}}\sin \theta =\frac{1}{2}\theta =\frac{\pi }{6}$