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. $18$
• B. $5$
• C. $2$
• D. $26$

Answer 1

The correct option is C $2$

General point on line : $2\lambda +3,-\lambda -2,3\lambda -4$For $\lambda =0\to A(3,-2,-4)$
$\lambda =1\to (5,-3,-1)$
Both $A$ & $B$ lie on plane $\Rightarrow 3l-2m+4=9---\left(1\right)$$5l-3m+1=9..............\left(2\right)$
eqn $\left(1\right)\times 3-$ eqn $\left(2\right)\times 2$$\Rightarrow 9l-10l+12-2=9\Rightarrow l=1$
and,
$\Rightarrow 2m=3-5=-2$$\Rightarrow m=-1$
then,
$\Rightarrow l^2+m^2=2$