Consider the three planes $P_{1}: 3x + 15y + 21z = 9$; $P_{2}: x - 3y - z = 5$; and $P_{3}: 2x + 10y + 14z = 5$. Then,which one of the following is true?

If two planes intersect,then the shortest distance between the planes is

The equation of the plane passing through $3 \hat{i}+2 \hat{j}+6 \hat{k}$ and parallel to the vectors $2 \hat{i}+\hat{j}+\hat{k}$ and $\hat{i}-\hat{j}+\hat{k}$ is

$A$ variable plane passes through the fixed point $(3, 2, 1)$ and meets $X, Y,$ and $Z$ axes at points $A, B,$ and $C$ respectively. $A$ plane is drawn parallel to the $YZ$-plane through $A$,a second plane is drawn parallel to the $ZX$-plane through $B$,and a third plane is drawn parallel to the $XY$-plane through $C$. Then the locus of the point of intersection of these three planes is:

If $(2, -1, 3)$ is the foot of the perpendicular drawn from the origin $(0, 0, 0)$ to a plane,then the equation of that plane is:

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