The area of the figure formed by the points (-1,-1,1);(1,1,1) and their mirror images on the plane 3x+2y+4z+1=0 is

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

Find the equation of the plane through the points (2,1,1) and (1,3,4) and perpendicular to the plane x-2y+4z=10 .

The equation of the plane passing through the points (1,1,1) and (1,-1,-1) and perpendicular to plane 2x-y+z=0 is

(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.

The equation of the plane which passes through the points (2, 1, -1) and (-1, 3, 4) and perpendicular to the plane x- 2y + 4z = 0 is

Find the vector equation of the plane through the points (2,1,-1) and (-1,3,4) and perpendicular to the plane x-2y+4z=10 .

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

Find the image of point (12,-1) in the plane 3x-5y+4z=5