Angle between Two Lines

In the following case, find the distance of the given point from the corresponding given plane.
Point                                        Plane

$\left(-6,0,0\right) 2x-3y+6z-2=0$

In the following case, find the distance of the given point from the corresponding given plane.
Point                                        Plane

$\left(2,3,-5\right) x+2y-2z=9$

In the following case, find the distance of the given point from the corresponding given plane.
Point                                        Plane

Find the distance of the given point from the corresponding given plane.
Point                                        Plane
$\left(0,0,0\right) 3x-4y+12z=3$

Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angles between them.
$4x+8y+z-8=0$ and $y+z-4=0$

Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angles between them.
$2x-y+3z-1=0$ and $2x-y+3z+3=0$

Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them.
 $2x-2y+4z+5=0$ and $3x-3y+6z-1=0$

Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them.
$2x+y+3z-2=0$ and $x-2y+5=0$

Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them.
$7x+5y+6z+30=0$ and $3x-y-10z+4=0$

Find the angle between the planes whose vector equations are
$\overrightarrow{r}·(2\widehat{i}+2\widehat{j}-3\widehat{k})=5$ and $\overrightarrow{r}·(3\widehat{i}-3\widehat{j}+5\widehat{k})=3$

Find the equation of the plane through the line of intersection of the planes $x+y+z=1$ and $2x+3y+4z=5$ which is perpendicular to the plane $x-y+z=0$.

Find the vector equation of the plane passing through the intersection of the planes $\overrightarrow{r}·\left(2\widehat{i}+2\widehat{j}-3\widehat{k}\right)=7,\overrightarrow{r}·\left(2\widehat{i}+5\widehat{j}+3\widehat{k}\right)=9$ and through the point $\left(2,1,3\right)$.

Find the equation of the plane through the intersection of the planes $3x-y+2z-4=0$ and $x+y+z-2=0$ and the point $\left(2,2,1\right)$.

Find the equation of the plane with intercept $3$ on the $y$-axis and parallel to $ZOX$ plane.

Find the intercepts cut off by the plane $2x+y-z=5$

Find the equation of the plane that passes through three points.
$\left(1,1,0\right),\left(1,2,1\right),\left(-2,2,-1\right)$

Find the equations of the planes that passes through three points.
$\left(1,1,-1\right),\left(6,4,-5\right),\left(-4,-2,3\right)$

Find the vector and Cartesian equation of the planes that passes through the point $\left(1,4,6\right)$ and the normal vector to the plane is $\widehat{i}-2\widehat{j}+\widehat{k}.$

Find the vector and Cartesian equation of the planes that passes through the point $\left(1,0,-2\right)$ and the normal to the plane is $\widehat{i}+\widehat{j}-\widehat{k}.$

Find the coordinates of the foot of the perpendicular drawn from the origin $5y+8=0$.