Question

The equation of the straight line passing through $(1,2,3)$ and perpendicular to the plane $x+2y-5z+9=0$ is

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

Answer 1

The correct option is A $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{-5}$

Equation of line passing through $(1,2,3)$ is :-

$\frac{x-1}{a}=\frac{y-2}{b}=\frac{2-3}{c}$

Now, since it is perpendicular to plane $x+2y-5z+9=0$, it is parallel to normal to plane.

$\therefore a=1,b=2,c=-5$

$\therefore$ equation of line is :-

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