The image point of $(5, 4, 6)$ in the plane $x + y + 2z - 15 = 0$ is

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

The angle between a diagonal of a cube and a diagonal of one of its faces,which are coterminus,is:

What is the angle subtended by an edge of a regular tetrahedron at its centre?

If $\alpha$ is the angle between any two diagonals of a cube and $\beta$ is the angle between a diagonal of a cube and a diagonal of its face, which intersects this diagonal of the cube, then $\cos \alpha + \cos^2 \beta =$

Let three points $A(2,3,4), B(3,4,2)$ and $C(4,2,3)$ in space be given. $A$ point $D$ in space is such that it is at a distance of $\sqrt{6}$ units from the $3$ given points. Then the volume of the tetrahedron $ABCD$ is -