The shortest distance from the plane `12 x+y+3z=327`to the sphere `x^2+y^2+z^2+4x-2y-6z=155` is

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

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

Find the value of lambda for which the plane x+y+z=sqrt(3)lambda touches the sphere x^2+y^2+z^2-2x-2y-2z=6.

The shortest distance between the lines 2x + y + z - 1 = 0 = 3x + y + 2z - 2 and x = y = z , is

The plane x+2y-z=4 cuts the sphere x^(2)+y^(2)+z^(2)-x+z-2=0 in a circle of radius

The locus of point such that the sum of the squares of its distances from the planes x+y+z=0, x-z=0 and x-2y+z=0 is 9 is (A) x^2+y^2+z^2=3 (B) x^2+y^2+z^2=6 (C) x^2+y^2+z^2=9 (D) x^2+y^2+z^2=12

Find the distance of the point (1,2,0) from the plane 4x+3y+12z+16=0

Find the distance between the planes 2x-y+2z=4 and 6x-3y+6z=2.

Two lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=(z)/(1) intersect at a point P. If the distance of P from the plane 2x-3y+6z=7 is lambda units, then the value of 49lambda is equal to

Find the shortest distance between the lines , (x-1)/2=(y-3)/4=(z+2)/1 and 3x-y-2z+4=0=2x+y+z+1 .