If the equation of the plane passing through the point $(3,2,5)$ and perpendicular to the planes $2x-3y+5z=7$ and $5x+2y-3z=11$ is $x+by+cz+d=0$,then $2b+3c+d=$

If the foot of the perpendicular drawn from the origin to a plane is $P(2,-1,4)$,then the equation of the plane is

The equation of the plane passing through the points $(2,3,1)$ and $(4,-5,3)$ and parallel to the $y$-axis is:

The length of the foot of the perpendicular from the point $P\left(1, \frac{3}{2}, 2\right)$ to the plane $2x - 2y + 4z + 17 = 0$ is

The equation of the plane passing through the point $(-1, 2, 1)$ and perpendicular to the line joining the points $(-3, 1, 2)$ and $(2, 3, 4)$ is $.........$

Let the image of the point $P(1, 2, 6)$ in the plane passing through the points $A(1, 2, 0)$,$B(1, 4, 1)$,and $C(0, 5, 1)$ be $Q(\alpha, \beta, \gamma)$. Then $(\alpha^2 + \beta^2 + \gamma^2)$ is equal to :