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

If $\left(\frac{9}{4}, \frac{5}{4}, \frac{15}{4}\right)$ is the centroid of a tetrahedron whose vertices are $(a, 2, 1), (1, b, 4), (4, 0, c)$ and $(1, 1, 7)$, then

$AB$ and $BC$ are diagonals of adjacent faces of a rectangular box with its center at the origin,and its edges parallel to the coordinate axes. If the angles $\angle BOC, \angle COA$,and $\angle AOB$ are $\alpha, \beta$,and $\gamma$ respectively,then $\cos \alpha + \cos \beta + \cos \gamma$ is equal to:

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 the orthocentre and the centroid of a triangle are at $(5,2,-6)$ and $(9,6,-4)$ respectively,then its circumcentre is

What is the angle between two diagonals of a cube?