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

If the orthocentre and the centroid of a triangle are $(-3,5,2)$ and $(3,3,4)$ respectively,then its circumcentre is

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 -

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

$A$ square $ABCD$ of diagonal $2a$ is folded along the diagonal $AC$ so that the planes $DAC$ and $BAC$ are at a right angle. The shortest distance between $DC$ and $AB$ 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