Question

The equation of the line, perpendicular to the plane $2x+3y+5z+1=0$ and passing through the point $(1,2,-3)$ is ______.

• A. $\frac{x-1}{2}=\frac{2-y}{-3}=\frac{z+3}{5}$
• B. $\frac{x-1}{2}=\frac{y+2}{3}=\frac{z+3}{5}$
• C. $\frac{x+1}{2}=\frac{y+2}{3}=\frac{z-3}{5}$
• D. $\frac{x-1}{2}=\frac{y-2}{-3}=\frac{z+3}{5}$

Answer 1

Answer: (A)

$\frac{x-1}{2}=\frac{2-y}{-3}=\frac{z+3}{5}$

The line perpendicular to the plane will have same direction ratios as the normal to the plane therefore the dr's of the line are $2,3,5$

and the given point is $(1,2,-3)$ therefore the equation of the line is

$\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+3}{5}$