The equation of the plane which bisects the line joining $(2, 3, 4)$ and $(6, 7, 8)$ is

If $A$ and $B$ are the feet of the perpendiculars drawn from point $Q(a, b, c)$ to the planes $yz$ and $zx$ respectively,then the equation of the plane passing through the points $A, B$ and the origin $O(0, 0, 0)$ is $.........$

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $5y + 8 = 0$.

If $l, m, n$ are the direction cosines of a normal to the plane passing through the points $(0, 1, 2)$, $(3, 0, 2)$, and $(4, 5, 0)$, then $|l| + |m| + |n| = $

$A$ vector $n$ of magnitude $8$ units is inclined to $x$-axis at $45^\circ$,$y$-axis at $60^\circ$ and an acute angle with $z$-axis. If a plane passes through a point $(\sqrt{2}, -1, 1)$ and is normal to $n$,then its equation in vector form is

The length of the perpendicular from the origin to the plane passing through three non-collinear points $a, b, c$ is