Find the equation of the plane passing through the point $(1, 2, -3)$ and parallel to the plane $3x - 5y + 2z = 11$.

The vector equation of a plane,which is at a distance of $8$ units from the origin and which is normal to the vector $\vec{n} = 2\hat{i} + \hat{j} + 2\hat{k}$,is

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:

$A$ plane is at a unit distance from the origin. It cuts the coordinate axes at $P, Q,$ and $R$ respectively. If the locus of the centroid of the $\Delta PQR$ is $\frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} = k$,then $k =$

The direction ratios of the normal to the plane passing through $(0,0,1)$,$(0,1,2)$,and $(1,0,3)$ are:

The equation of the plane whose intercepts on $x, y, z$ axes are $1, 2, 4$ respectively is