The equation of the plane mid-parallel to the planes $2x - 3y + 6z + 21 = 0$ and $2x - 3y + 6z - 14 = 0$ is given by

The equation $axy + byz = cy$ represents the locus of the points which lie on

If $A$ and $B$ are the feet of the perpendiculars drawn from $(1, 2, 3)$ to planes $YZ$ and $ZX$ respectively, then the equation of the plane passing through the points $A$, $B$ and the origin $(0, 0, 0)$ is

The equation of the plane passing through the point $(1, 2, 1)$ and perpendicular to the planes $x + 2y + 2z - 7 = 0$ and $3x + 3y + 2z - 5 = 0$ is

The volume of the tetrahedron (in cubic units) formed by the plane $2x + y + z = K$ and the coordinate planes is $\frac{2V^3}{3}$, then $K:V =$

$A$ plane $\pi_1$ passing through the point $3 \hat{i}-7 \hat{j}+5 \hat{k}$ is perpendicular to the vector $\hat{i}+2 \hat{j}-2 \hat{k}$ and another plane $\pi_2$ passing through the point $2 \hat{i}+7 \hat{j}-8 \hat{k}$ is perpendicular to the vector $3 \hat{i}+2 \hat{j}+6 \hat{k}$. If $p_1$ and $p_2$ are the perpendicular distances from the origin to the planes $\pi_1$ and $\pi_2$ respectively, then $p_1-p_2=$