$A(27, -243, 81)$ is a point in space. $B, C, D$ are images of $A$ with respect to $XY, YZ$,and $ZX$ planes respectively. If the centroid of the triangle $BCD$ is $(\alpha, \beta, \gamma)$,then $\alpha + \beta + \gamma =$

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

If a line makes angles $\alpha, \beta, \gamma, \delta$ with the four diagonals of a cube,then find the value of $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma + \sin^2 \delta$.

Three identical balls of radius $2 \, cm$ each are placed on a table such that they touch each other as well as the table. Now a fourth ball of the same radius is placed above these three balls. The height of the highest point on the fourth ball above the table is -

The length of the internal bisector of angle $A$ in $\triangle ABC$ with vertices $A(4,7,8)$,$B(2,3,4)$ and $C(2,5,7)$ is

The angle between two diagonals of a cube is