Show that the points `(1,-1,3) and (3, 4, 3)` are equidistant from the plane `5x +2y + -7z + 8 = 0.`

Show that the points (1, 1, 1) and (-3, 0, 1) are equidistant from the plane 3x+4y-12 z+13=0.

Show that the points (-3,0,1) and (1,1,1) are equidistant from the plane 3x+4y-12z+13=0 .

Show that the points (1, 1, 1) and (-3, 0, 1) are equidistant from the plane barr *(3hati + 4hatj - 12hatk) + 13 = 0

If the points (2,1) and (1,-2) are equidistant from the point (x,y), show that x+3y=0

The ratio of the distances from the points (1,-1,3) and (3,3,3) to the plane 5x+2y-7z+9=0 is

Ifthe points (1,1,lambda) and (-3,0,1) are equidistant from the plane,3x+4y-12z+13=0, then lambda satisfiesthe equation

(i) Find the equation of the plane passing through (1,-1,2) and perpendicular to the planes : 2 x + 3y - 2z = 5 , x + 2y - 3z = 8 . (ii) find the equation of the plane passing through the point (1,1,-1) and perpendicular to each of the planes : x + 2y + 3z - 7 = 0 and 2x - 3y + 4z = 0 . (iii) Find the equation of the plane passing through the point (-1,-1,2) and perpendicular to the planes : 3x + 2y - 3z = 1 and 5x - 4y + z = 5.