Show that the plane `2x-2y+z+12=0` touches the sphere `x^2+y^2+z^2-2x-4y+2z-3=0.`

The shortest distance from the plane 12 x+4y+3z=327 to the sphere x^2+y^2+z^2+4x-2y-6z=155 is a. 39 b. 26 c. 41-4/(13) d. 13

If plane 2x+3y+6z+k=0 is tangent to the sphere x^(2)+y^(2)+z^(2)+2x-2y+2z-6=0 , then a value of k is

A plane passes through a fixed point (a ,b ,c)dot Show that the locus of the foot of the perpendicular to it from the origin is the sphere x^2+y^2+z^2-a x-b y-c z=0.

The radius of the circle in which the sphere x^(2)+y^2+z^2+2z-2y-4z-19=0 is cut by the plane x+2y+2z+7=0 is a. 2 b. 3 c. 4 d. 1

Find the equation of the plane through the intersection of the planes 2x - 3y + z - = 0 and x - y + z + 1 = 0 and perpendicular to the plane x + 2y - 3z + 6 = 0.

The planes 2x -y+4z=5 and 5x-2.5y+10z=6 are

Find the value of m for which thestraight line 3x-2y+z+3=0=4x+3y+4z+1 is parallel to the plane 2x-y+m z-2=0.

The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2+z^2-3x+3y+4z=8 is the same as the intersection of one of the spheres and the plane a. x-y-z=1 b. x-2y-z=1 c. x-y-2z=1 d. 2x-y-z=1

The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2=z^2-3x+3y+4z=8 is the same as the intersection of one of the spheres and the plane a. x-y-z=1 b. x-2y-z=1 c. x-y-2z=1 d. 2x-y-z=1

Find the distance between the parallel planes x-2y-2z=3 and 2x-4y-4z=7 .