Condition for a Line to Lie on a Plane

Q.

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

1. 26

2. 18

3. 5

4. 2

Q. If for some $\alpha$ and $\beta$ in $R$, the intersection of the following three planes
$x+4y-2z=1x+7y-5z=\beta x+5y+\alpha z=5$
is a line in $R^3$, then $\alpha +\beta$ is equal to :

1. $0$
2. $10$
3. $-10$
4. $2$

Q. $\mathrm{Line}\frac{x-1}{5}=\frac{y+5}{-2}=\frac{z+1}{-1}\mathrm{lies}\mathrm{on}\mathrm{the}\mathrm{plane}2x+5y-z+5=0$

1. True
2. False