Question

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

• A. 26
• B. 18
• C. 5
• D. 2

Answer 1

Answer: (D)

Point on line is $P=(3,-2,-4)$
‘$P$’ lies on $\ell x+my-z=9$
$\Rightarrow 3\ell -2m+4=9$
$3\ell -2m=5$ .....(1)
As line lies on plane
$\Rightarrow 2\times \ell +m\times (-1)+3\times (-1)=0$
$2\ell -m=3$ ....(3)
Solving $\ell =1,m=-1$
So, ${\ell }^2+m^2=2$