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

Given line lies in the plane lx + my – z = 0

$\therefore$ point (3,–2,–4) lies on the plane $3\mathrm{l}-2\mathrm{m}=5 \dots .\left(\mathrm{i}\right)$

$\Rightarrow$Also $2\mathrm{l}-\mathrm{m}-3=0\Rightarrow 2\mathrm{l}-\mathrm{m}=3 ....\left(\mathrm{ii}\right)$

From (i) and (ii), $\mathrm{l}=1\text{ and }\mathrm{m}=-1$