In the following cases, find the distance of each of the given points from the corresponding given plane.
`{:("Point","Plane"),("a. (0,0,0),3x-4y+12z=3),(b. (3,-2,1),2x-y+2z+3=0),(c.(2,3,-5),x+2y-2z=9),(d.(-6,0,0),2x-3y+6z-2=0):}`

Find the distance of the z-axis from the image of the point M(2-3,3) in the plane x-2y-z+1=0.

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin. a.2x+3y+4z-12=0 b.3y+4z-6=0 c. x+y+z=1 d. 5y+8=0

Find the coordinates of the foot of the perpendicular P from the origin to the plane 2x-3y+4z-6=0

In each of the following cases , determine the direction cosines of the normal to the plane and the distance from the origin . a. z=2 , b.x+y+z=1 , c. 2x+3y-z=5, d.5y+8=0

Find the distance of the point (1,0,-3) from the plane x-y-z=9 measured parallel to the line (x-2)/2=(y+2)/2=(z-6)/(-6)dot

Find the equation of the image of the plane x-2y+2z-3=0 in plane x+y+z-1=0.

Distance from the origin to the plane 3x - 6y + 2z + 7 = 0 is

Find the distance of the point P(3,8,2) from the line 1/2(x-1)=1/4(y-3)=1/3(z-2) measured parallel to the plane 3x+2y-2z+15=0.

In the follwing cases , determine whether the given planes are parallel or perpendicular and in case they are neither , find the angles between them. a. 7x+5y+6z+30=0 and 3x-y-10z+4=0 b. 2x+y+3z-2=0 and x-2y+5=0 c. 2x-2y +4z +5=0 and 3x-3y+6z-1=0 d. 2x-y+3z-1=0 and 2x-y+3z+3=0 e. 4x+8y+z-8=0 and y+z-4=0