Find the equation of the plane through the intersection of the planes `x+3y+6=0 and 3x-y-4z=0`, whose perpendicular distance from the origin is unity.

Find the equation of the line through the point of intersection of, the lines x-3y + 1 = 0 and 2x + 5y-9-0 and whose distance from the origin is sqrt5

Find the equation of the line through the point of intersection of, the lines x-3y + 1 = 0 and 2x + 5y-9-0 and whose distance from the origin is sqrt5

Find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0

Find the equation of the plane through the intersection of the planes 3x-y+2z-4=0 and x+y+z-2=0 and the point (2,2,1).

The equation of the plane through the intersection of the planes x+y+z=1 and 2x+3y-z+4 = 0 and parallel to x-axis is

The equation of the plane through the intersection of the planes x+y+z=1 and 2x+3y-z+4 = 0 and parallel to x-axis is

Find the equation of the plane through the intersection of the planes 3x-y+2z-4=0 and x+y+z-2=0 and the point (2, 2, 1).

Find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0 . Then find the distance of plane thus obtained from the point A(1,3,6) .

Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5, which is perpendicular to the plane x - y + z = 0.

Find the equation of the plane passing through the intersection of the planes 2x+3y-z+1=0 and x+y-2z+3=0 and perpendicular to the plane 3x-y-2z-4=0.