The distance between two parallel planes $2x + y + 2z = 8$ and $4x + 2y + 4z + 5 = 0$ is:

$A$ line joining the points $(1, 2, 0)$ and $(4, 13, 5)$ is perpendicular to a plane. Then the coefficients of $x, y$ and $z$ in the equation of the plane are respectively

The values of $a$ for which the two points $(1, a, 1)$ and $(-3, 0, a)$ lie on the opposite sides of the plane $3x + 4y - 12z + 13 = 0$ satisfy:

The Cartesian equation of the plane passing through the point $A(7, 8, 6)$ and parallel to the $XY$-plane is:

$A$ plane is parallel to two lines,whose direction ratios are $1, 0, -1$ and $-1, 1, 0$ and it contains the point $(1, 1, 1)$. If it cuts coordinate axes ($X, Y, Z$-axes respectively) at $A, B, C$,then the volume of the tetrahedron $OABC$ is (in cubic units):

The equation of the plane passing through the point $(2, 0, 5)$ and parallel to the vectors $\hat{i} - \hat{j} + \hat{k}$ and $3\hat{i} + 2\hat{j} + \hat{k}$ is: