Equation of Plane

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 the point $(\mathrm{1,1},1)$ and perpendicular to the planes $2x+y-2z=5$ and $3x-6y-2z=7$ is

If the foot of the perpendicular drawn from the point $(0,0,0)$ to the plane is $(4,-2,-5)$ then the equation of the plane is …..

If $A$ and $B$ are foot of perpendicular drawn from point $Q\left(a, b, c\right)$ to the planes $yz$ and $zx$ , then equation of plane through the points $A,B$ and $O$ is _______

The equation of the plane through $\left(-1,1,2\right),$ whose normal makes equal acute angle with co-ordinate axes is

The coordinates of the foot of the perpendicular drawn from the origin to the plane $5y+8=0$ are

The coordinates of the foot of the perpendicular drawn from the origin to the plane $2x+3y+4z-12=0$ are

The direction cosines of the normal to the plane $3x-6y+2z=7$ are

The equation of the plane which passes through the point $(2,-3,7)$and makes equal intercepts on the coordinate axes is

The equation of the plane whose intercepts on the coordinate axes are $2,-4$ and $5$ respectively is

The equation of the plane passing through the group of points $A(2, 2, -1), B(3, 4, 2)$ and $C(7, 0, 6)$ is