Plane and a Point

For all $d, 0<d<1,$ which one of the following points is the reflection of the point $\left(d,2d,3d\right)$ in the plane passing through the points $\left(1,0,0\right), \left(0,1,0\right)$ and $\left(0,0,1\right)$?

A variable plane is at a constant distance $p$ from the origin $O$ and meets the set of rectangular axes $O{X}_i\left(i=1,2,3\right)$ at point $A_i\left(i=1,2,3\right)$, respectively. If planes are drawn through $A_1, A_2 \text{and} A_3$, which are parallel to the coordinate planes, then the locus of their point of intersection is

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

Let $A\left(p,q,r\right)$ be a point on the plane $2x+y+z=5$, then the least value of  $6\left(p^2+q^2+r^2\right)=$

The foot of the perpendicular from $\left(0, 0, 0\right)$ on the plane $2x-2y-5z-33=0$ is at the point.

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

Foot of perpendicular from $\left(-1,3,4\right)$ on the plane $x-2y=0,$ is

If the reflection of the point $P\left(1, 0, 0\right)$ in the line $\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+10}{8}$ is $\left(\alpha , \beta , \gamma \right)$ then find value of $-\left(\alpha +\beta +\gamma \right)$.

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

The foot of the perpendicular drawn from the origin to the plane $x+y+3z-4=0$ is

Vertices of a parallelogram taken in order are $A(2,-1,4), B(1,0,-1), C(1,2,3)$ and $D$. Distance of the point $P (8,2,-12)$ from the plane of the parallelogram is -

The ratio of the distance from $\left(-1,1,3\right)$ and $\left(3,2,1\right)$ to the plane $2x+5y-7z+9=0$ is

The reflection of the plane $2x-3y+4z-3=0$ in the plane $x-y+z-3=0$ is the plane

The length of perpendicular from origin to the plane $r·\left(3\hat{i}-4\hat{j}+12\hat{k}\right)=5$ is

If the image of the point $A\left(1,2,-3\right)$ in the plane $2x+3y-z=8$ measured parallel to the line $\frac{x}{1}=\frac{1-y}{1}=\frac{z}{2}$ is $B$, then $AB$ is equal to

A plane $P$ is perpendicular to the vector $\overrightarrow{A}=2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+6\hat{\mathrm{k}}$ and contains the terminal point of the vector $\overrightarrow{\mathit{B}}=\hat{\mathrm{i}}+5\hat{\mathrm{j}}+3\hat{\mathrm{k}}$. The perpendicular distance from the origin to the plane $P$ is equal to