Question

The angle between the straight line
$\frac{x-1}{2}=\frac{y+3}{-1}=\frac{z-5}{2}$ and plane $4x-2y+4z=9$ is

• A. $60^{\circ }$
• B. $90^{\circ }$
• C. $45^{\circ }$
• D. $30^{\circ }$

Answer 1

Answer: (B)

Direction ratio of the line are $(2,-1,2)$ and direction ratio of normal to the plane is $(4,-2,4)$
$cos\left(90^{\circ }-\theta \right)=\frac{|2\left(4\right)+\left(-1\right)\left(-2\right)+2\left(4\right)|}{\sqrt{2^2+{\left(-1\right)}^2+2^2}\sqrt{4^2+{\left(-2\right)}^2+4^2}}$
$sin\theta =\frac{8+2+8}{3\times 6}=\frac{18}{18}$
$\Rightarrow sin\theta =1$
$\theta =90^{\circ }$.