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

Answer: (A)

$\frac{\pi }{3}$

$\text{c}os\theta =\frac{1.0+1.1+0.1}{\left(\surd \right(1^2+1^2+0^2).(\surd 0^2+1^2+1^2)}$

$\text{c}os\theta =\frac{1}{\surd 2.\surd 2}$

$\text{c}os\theta =\frac{1}{2}$

$\theta =\frac{\pi }{3}$