consider the family of lines through the point (1,2, 2) and lying in the plane `2x-y+z=2` family which is at a maximum distance from the point (2, 1,1) is

A plane passes through the point (1,-2,3) and is parallel to the plane 2x-2y+z=0 . The distance of the point (-1,2,0) from the plane, is

A line joining the points (1,1,1) and (2,2,2) intersect the plane x+y+z=9 at the point

Equation of a plane passing through the lines 2x-y+z=3 and 3x+y+z=5 and which is at a distance of (1)/(sqrt(6)) from the point(2, 1, -1) is

Equation of a plane passing through the lines 2x-y+z=3 and 3x+y+z=5 and which is at a distance of (1)/(sqrt(6)) from the point(2, 1, -1) is

If the lines L_(1):(x-1)/(3)=(y-lambda)/(1)=(z-3)/(2) and L_(2):(x-3)/(1)=(y-1)/(2)=(z-2)/(3) are coplanar, then the equation of the plane passing through the point of intersection of L_(1)&L_(2) which is at a maximum distance from the origin is

A plane passes through the point (1,-2,3) and is parallel to the plane 2x - 2y + z=0. The distance of the point (-1, 2, 0) from the plane is