The plane `4x+7y+4z+81=0` is rotated through a right angle about its line of intersection with the plane `5x+3y+10 z=25.` The equation of the plane in its new position is a. `x-4y+6z=106` b. `x-8y+13 z=103` c. `x-4y+6z=110` d. `x-8y+13 z=105`

The plane denoted by P_(1) : 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with the plane P_(2) : 5x+3y+ 10 z = 25 . If the plane in its new position is denoted by P , and the distance of this plane from the origin is d, then find the value of [k//2] (where [*] represents greatest integer less than or equal to k).

The x-y plane is rotated about its line of intersection with the y-z plane by 45^0 , then the equation of the new plane is/are a. z+x=0 b. z-y=0 c. x+y+z=0 d. z-x=0

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

The direction ratios of the line, given by the planes x - y + z - 5 = 0, x - 3y - 6 = 0 are

Show that the disease of the point of intersection of the line (x-2)/3=(y+1)/4=(z-2)/12 and the plane (x-y+z=5) from the point (-1,-5,-10) is 13 units.

The equation of the plane through the line of intersection of the planes ax + by+cz + d= 0 and a'x + b'y+c'z + d'= 0 parallel to the line y=0 and z=0 is

The equation of the plane through the line of intersection of the planes ax + by+cz + d= 0 and a'x + b'y+c'z + d'= 0 parallel to the line y=0 and z=0 is

Find the equation of the plane containing the line of intersection of the planes x + y + z - 6 = 0 and 2x + 3y + 4z + 5 = 0 and passing through the point (1,1,1)

The planes 2x -y+4z=5 and 5x-2.5y+10z=6 are