Equation of Plane in 3D

If the coordinates of point $P$ are $\left(3,2,-1\right)$, then find the equation of plane through $P$ at right angle to the line $OP$, where $O$ is origin.

Let $A, B, C$ be the points $2\hat{i}-\hat{j}+\hat{i}, \hat{i}+2\hat{j}+\hat{k}$ and $3\hat{i}+\hat{j}+2\hat{k}$ respectively. Find the shortest distance between plane $OAC$ to point $B$.

If from a point $Q$ lying on plane $P$ in $1^{\mathrm{st}}$ octant the distances of planes $x=0, y=0, z=0$ are $1,1 \& 2$ respectively, then vector equation of line passing through origin and parallel to normal vector of plane $P$ is (where, $\lambda \in R)$

Let $\overrightarrow{AB}=\hat{i}+\hat{j}-3\hat{k}$, $\overrightarrow{AC}=3\hat{i}+\hat{j}+4\hat{k}$ and $\overrightarrow{AD}=2\hat{i}-\hat{k}$ are three co-terminus edges of a tetrahedron $ABCD$. If position vector of the centre of tetrahedron is $\hat{i}+2\hat{j}+3\hat{k}$, then

Let $L$ be the projection of the line $\frac{x+1}{2}=\frac{y+2}{3}=\frac{z+3}{4}$ on the plane $x-2y+3z-4=0$. Then the equation of the plane passing through $L$ and parallel to the line $x=y=z$ is

If the volume of a tetrahedron formed by the three coordinate planes and a variable plane is always $4$ cubic units, then the locus of the foot of the perpendicular from the origin to this variable plane is ${\left(x^2+y^2+z^2\right)}^3=kxyz$, where $k=$

Define plane and find distance from $\left(1,2,3\right)$ to $2x+3y-4=0$.

Define plane and find distance from $\left(1,2,3\right)$ to $3x+2y-4=0$.

Define plane and find distance from $\left(1,2,3\right)$ to $2z+x-2=0$.

Define plane and find distance from $\left(1,2,3\right)$ to $2x+3z-4=0$.

How a plane is determined in $3D$ with respect to another plane. Find the distance from $\left(1,2,3\right)$ to plane $2x+3y-4=0$.

How a plane is determined in $3D$ with respect to another plane. Find the distance from $\left(1,2,3\right)$ to plane $3x+2y-4=0$.

Define plane and find distance from $\left(1,2,3\right)$ to $2x+3y+4z-5=0$.

The equation of the plane passing through $(-2,1,3)$ and having $(3,-5,4)$ as direction ratios of its normal is

The equation of the plane passing through $(2,3,4)$ and perpendicular to $X-$axis is

Find the constant $k$ so that the planes $x-2y+kz=0$ and $2x+5y-z=0$ are at right angles.

If the foot of the perpendicular from origin to the plane is $(1,3,-5)$ then the equation of the plane is

If the equation of the plane passing through the point $(-1, 2, 1)$ and perpendicular to the line joining the points $(-3,1,2)$ and $(2,3,4)$ is $5x+2y+2z-k=0$, then find the value of $k$.