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 $(4, -2, 4)$
$cos\left(90^{\circ}-\theta\right)=\frac{\left|2\left(4\right)+\left(-1\right)\left(-2\right)+2\left(4\right)\right|}{\sqrt{2^{2}+\left(-1\right)^{2}+2^{2}}\,\sqrt{4^{2}+\left(-2\right)^{2}+4^{2}}}$
$sin\theta=\frac{8+2+8}{3 \times 6}=\frac{18}{18}$
$\Rightarrow sin\theta=1$
$\theta=90^{\circ}$.