Condition for a Line to Lie on a Plane

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. The distance of the point (1, 0, 2) from the point of intersection of the line
$\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$
and the plane $x-y+z=16$, is

1. $2\sqrt{14}$
2. 8
3. $3\sqrt{21}$
4. 13

Q. If the line $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}$ intersects the plane $2x+3y-z+13=0$ at a point $P$ and the plane $3x+y+4z=16$ at a point $Q,$ then $PQ$ is equal to :

1. $\sqrt{14}$
2. $2\sqrt{14}$
3. $14$
4. $2\sqrt{7}$

Q.

Write a linear function that relates $\mathrm{y}$ to $\mathrm{x}$.