Find the equation of the set of points which are equidistant from the points $(1, 2, 3)$ and $(3, 2, -1)$.

If $M$ is the foot of the perpendicular drawn from $P(1,2,-1)$ to the plane passing through the point $A(3,-2,1)$ and perpendicular to the vector $4 \hat{i}+7 \hat{j}-4 \hat{k}$,then the length of $PM$ is

If the foot of the perpendicular from $(0,0,0)$ to the plane is $(1,2,2)$,then the equation of the plane is

The distance of the plane $6x - 3y + 2z - 14 = 0$ from the origin is

$A$ point moves such that its distances from the points $(3, 4, -2)$ and $(2, 3, -3)$ remain equal. The locus of the point is

$A$ plane $\Pi$ passes through the points $A=(0,0,2)$,$B=(1,0,1)$,and $C=(3,1,1)$. If the plane $\Pi$ makes angles $\alpha$ and $\beta$ with the $XY$ and $XZ$-coordinate planes respectively,then $\sin^2 \alpha + \sin^2 \beta =$