Question

If the line, $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}$ lies in the plane, lx+my-z = 9, then $l^2+m^2$ is equal to

• A. 26
• B. 18
• C. 5
• D. 2

Answer 1

The correct option is D

2

Since , the line $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}$ lies in the plane $lx+my-z=9$, therefore we have $2l-m-3=0$ [$\because$ normal will be perpendicular to the line ]
$\Rightarrow 2l-m=5.....\left(i\right)\text{and}3l-2m+4=9$ [$\because$ point $(3,-2,-4)$ lies on the plane ]
$\Rightarrow 3l-2m=5\left(ii\right)$
On solving Eqs. (i) and (ii), we get
$l=1$ and $m=-1$
$\therefore l^2+m^2=2$