Prove that the planes `12x-15y+16z-28=0, 6x + 6y -7z- 8= 0` and `2x + 35y-39z + 12 = 0` have a common line of intersection.

Consider three planes : 2x+py+6z=8, x+2y+qz=5 and x+y+3z=4 Q. Three planes do not have any common point of intersection if :

The planes 2x + 5y + 3z = 0, x-y+4z = 2 and7y-5z + 4 = 0

If 7x + 6y - 2z = 0, 3x + 4y + 2z = 0, x - 2y - 6z = 0 then which option is correct

Consider the planes 3x-6y-2z-15 =0 and 2x+y-2z - 5=0 Statement 1:The parametric equations of the line intersection of the given planes are x=3+14 t ,y=2t ,z=15 tdot Statement 2: The vector 14 hat i+2 hat j+15 hat k is parallel to the line of intersection of the given planes.

The circles x^2 + y^2 + 6x + 6y = 0 and x^2 + y^2 - 12x - 12y = 0

Show that the planes 2x+6y-6z=7\ a n d\ 3x+4y+5z=8 are at right angles.

The lines x + y + z - 3 = 0 = 2x - y + 5z - 6 and x - y - z + 1 = 0 = 2x + 3y + 7z - k are coplanar then k equals

Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z-4 and is parallel to the line of intersection of the planes 2x + 3y +z=1 and x + 3y + 2z = 2 be x + Ay + Bz + C=0 Compute the value of |A+B+C| .

Find the angle between two planes 2x+y-5z=0 and 4x -3y+7z=0

Show that the plane 2x-2y+z+12=0 touches the sphere x^2+y^2+z^2-2x-4y+2z-3=0.