The equation of the plane passing through $(1, 2, 3)$ and parallel to the plane $2x + 3y - 4z = 0$ is

The equation of the plane passing through the points $(2,3,1)$ and $(4,-5,3)$ and parallel to the $y$-axis is:

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

If the points $(1, -1, \lambda)$ and $(-3, 0, 1)$ are equidistant from the plane $3x - 4y - 12z + 13 = 0$,then the sum of all possible values of $\lambda$ is

Find the Cartesian equation of the plane $\vec{r} = (1 + \lambda - \mu)\hat{i} + (2 - \lambda)\hat{j} + (3 - 2\lambda + 2\mu)\hat{k}$.

If $(x, y, z)$ is an arbitrary point lying on a plane $P$ which passes through the points $(42, 0, 0)$,$(0, 42, 0)$,and $(0, 0, 42)$,then the value of the expression $3 + \frac{x-11}{(y-19)^{2}(z-12)^{2}} + \frac{y-19}{(x-11)^{2}(z-12)^{2}} + \frac{z-12}{(x-11)^{2}(y-19)^{2}} - \frac{x+y+z}{14(x-11)(y-19)(z-12)}$ is: