Find the distance of the point $P(-\hat{i} + 2\hat{j} + 6\hat{k})$ from the line passing through the point $A(2, 3, -4)$ and parallel to the vector $\vec{v} = 6\hat{i} + 3\hat{j} - 4\hat{k}$.

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

If the direction cosines of two lines inclined at an angle $\theta$ are $(l_1, m_1, n_1)$ and $(l_2, m_2, n_2)$,then the direction cosines of the internal bisector of the angle between the lines are:

If the three consecutive vertices of a parallelogram are $A(1, 2, 3)$,$B(-1, -2, -1)$,and $C(2, 3, 2)$,then its fourth vertex 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

What is the angle between two diagonals of a cube?