The transformed equation of $2x^2 + 3y^2 - z^2 - 8x + 18y + 2z + 9 = 0$ when the axes are translated to the point $(2, -3, 1)$ is

If $A=(2,3,4)$ and $B=(-2,3,4)$,then the locus of a point $P(x,y,z)$ such that $PA+PB=4$ is

Let $ABCD$ be a tetrahedron such that the edges $AB, AC$ and $AD$ are mutually perpendicular. Let the areas of the triangles $ABC, ACD$ and $ADB$ be $5, 6$ and $7$ square units respectively. Then the area (in square units) of the $\triangle BCD$ is equal to :

The equation of the locus of a point whose distance from the $XY$-plane is twice its distance from the $Z$-axis is:

$\Pi_1, \Pi_2, \Pi_3$ are three planes which are respectively parallel to the $YZ, ZX$ and $XY$ planes at distances $a, b$ and $c$ forming a rectangular parallelopiped. $d_1$ is a diagonal of the face of $XY$-plane not passing through the origin and $d_2$ is a diagonal of the plane $\Pi_2$ coterminous with $d_1$. If none of the coordinates of the vertices of the parallelopiped are negative, then the angle between $d_1$ and $d_2$ is

The incenter of the triangle $ABC$,whose vertices are $A(0,2,1)$,$B(-2,0,0)$,and $C(-2,0,2)$ is