$A$ point on the plane passing through the points $(\sqrt{2}, 1, 4)$,$(0, -1, 0)$ and $(0, 0, 1)$ is

What is the equation of the plane passing through the point $(1, 1, 0)$ and perpendicular to the line $\vec{r} = (2, 3, 4) + k(3, 4, 5)$,where $k \in R$?

The distance between the parallel planes $ax + by + cz + d = 0$ and $ax + by + cz + d' = 0$ is:

If the equation of the plane passing through the point $(3,2,5)$ and perpendicular to the planes $2x-3y+5z=7$ and $5x+2y-3z=11$ is $x+by+cz+d=0$,then $2b+3c+d=$

Find the vector and cartesian equations of the plane which passes through the point $(5, 2, -4)$ and is perpendicular to the line with direction ratios $2, 3, -1$.

The equation of the plane passing through the point $(2, -1, -3)$ and parallel to the lines $\frac{x-1}{3} = \frac{y+2}{2} = \frac{z}{-4}$ and $\frac{x}{2} = \frac{y-1}{-3} = \frac{z-2}{2}$ is