Distance of a Point From a Plane

Find the distance of the point $P(3, 4, 5)$ from $z$-axis.

The distance of point $(3,-2,1)$ to plane $3x-4y+12z=3$ measured in the direction of line $\frac{x-3}{3}=\frac{y+2}{-4}=\frac{z-1}{12}$ is

If the distance between plane $2x+5y+4z=12$ and point $M\left(2,5,7\right)$ is $\sqrt{k}$ units. What is the value of $k$.

Find the distance[Units] between plane $2x+4y-4z=6$ and point $M\left(0,3,6\right)$.

If the distance of the point $\hat{i}+2\hat{j}-\hat{k}$ from the plane $\overrightarrow{r}.\left(\hat{i}-2\hat{j}+4\hat{k}\right)=10$ is $\frac{a}{\sqrt{21}}$, then $a=$

The distance of the point $(1,2,-1)$ from the plane $x-2y+4z-10=0$ is

The distance of the point $\left(\mathrm{2,3},2\right)$ from the plane $3x+4y+4z=23$ measured parallel to the line $\frac{x+3}{1}=\frac{y-6}{-2}=\frac{z-1}{1}$ is

The distance of the point $\left(2, 3, -5\right)$ from the plane $x+2y-2z=9$ is

The length of the perpendicular from the origin to the plane $3x+4y+12z=52$ is

If for a plane $x, y, z$ intercepts are $8,4,4$ respectively, then the length of the perpendicular from the origin on to the plane is