Question

The line perpendicular to the plane $2x-y+5z=4$ passing through the point $(-1,0,1)$ is

• A. $\frac{x+1}{2}=–y=\frac{[z–1]}{–5}$
• B. $\frac{x+1}{-2}=y=\frac{[z–1]}{–5}$
• C. $\frac{x+1}{2}=-y=\frac{[z–1]}{5}$
• D. $\frac{x+1}{2}=y=\frac{[z–1]}{–5}$

Answer 1

The correct option is C

$\frac{x+1}{2}=-y=\frac{[z–1]}{5}$

Find the equation of the line

Given,

1. The line is perpendicular to the plane $2x-y+5z=4$.
2. The line passes through the point $(-1,0,1)$.

The equation of the line passing through the plane $ax+by+cz=0$ at the point $(x_1,y_1,z_1)$ is

$\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$

The equation of the line passing through the given point and plane is

$$\begin{gathered} \Rightarrow \frac{x-(-1)}{2}=\frac{y-0}{-1}=\frac{z-1}{5} \\ \Rightarrow \frac{x+1}{2}=-y=\frac{z-1}{5} \end{gathered}$$

Hence, the correct option is $C$, $\frac{x+1}{2}=-y=\frac{[z–1]}{5}$.