Question

Equation of line passing through $(2,3,-4)$ & perpendicular to $XZ$ plane is

• A. $\frac{x-2}{1}=\frac{z+4}{1},y=3$
• B. $x=2,y=3+\lambda ,z=-4$
• C. $x=-2,y=-3+\lambda ,z=4$
• D. $x=-2,y=\lambda +3,z=4$

Answer 1

The correct option is A $\frac{x-2}{1}=\frac{z+4}{1},y=3$

$\frac{x-x_1}{h_1}=\frac{y-y_1}{k_1}=\frac{z-z_1}{l_1}=p$ where p is a constant and $(x_1,y_1,z_1)$.

Given $(x_1,y_1,z_1)$ by using perpendicular to $x-z$ plane condition that is

$\frac{x-2}{1}=\frac{y-3}{0}=\frac{z+4}{1}=p$

because the d.r's of the x-z plane $(1,\frac{1}{0},1)$ so the d.r's of the plane perpendicular to it has d.r's $(1,0,1)$.

$\frac{x-2}{1}=\frac{z+4}{1},y=3$