Question

The equations of a line passing through the point $(-1,0,3)$ and perpendicular to the plane $4x+3y-5z=12$ are

• A. $\frac{x-1}{4}=\frac{y}{3}=\frac{z+3}{-5}$
• B. $5(3x-1)=20(y-1)=-4(z-4)$
• C. $\frac{x+1}{-5}=\frac{y}{3}=\frac{z-3}{4}$
• D. none of these

Answer 1

The correct option is D none of these

The line perpendicular to the plane $4x+3y-5z=12$ is parallel to the normal to the plane.
$\Rightarrow$ Direction ratios of line are $(4,3,-5)$.
given that line is passing through $(-1,0,3)$
$\therefore$ Equation of line is $\frac{x+1}{4}=\frac{y}{3}=\frac{z-3}{-5}$
Hence, option D.