Question

If the line $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}$ lines 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 A $26$

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

The line passing through $(3,-2,-4)$

$(3,-2,-4)$ lies on the plane $lx+my-z=9$

$\therefore 3l-3m-(-4)=9$

$\Rightarrow 3l-2m=5$. . . eq.2

Direction ratios of eq.1 are : $2,-1,3$

Since eq.1 lies on the plane $lx+my-z=9$

$\therefore l\left(2\right)+m(-1)+(-1).\left(3\right)=0$

$\Rightarrow 2l-m-3=0$

$\Rightarrow 2l-m=3$. . . eq.3

Solving eq.2 & eq.3 , we get,

$l=1,m=-1$

$\therefore l^2+m^2=(1{)}^2+(-1{)}^2=2$