"Show that `a x+b y+r=0,b y+c z+p=0a n dc z+a x+q=0` are perpendicular to `x-y ,y-za n dz-x` planes,

Show that ax+by+r=0,by+cz+p=0 and cz+ax+q=0 are perpendicular to x-y,y-z and z-x planes, respectively.

Show that |a b c a+2x b+2y c+2z x y z|=0

The plane x + 3y + 13 = 0 passes through the line of intersection of the planes 2x - 8y + 4z = p and 3x - 5y + 4z + 10 = 0 If the plane is perpendicular to the plane , 3x - y - 2z - 4 = 0 then the value of p is equal to

The plane x + 3y + 13 = 0 passes through the line of intersection of the planes 2x - 8y + 4z = p and 3x - 5y + 4z + 10 =0 . If the plane is perpendicular to the plane 3x - y - 2z - 4 = 0 , then the value of p is equal to

Show that the normal to the following planes are perpendicular to each other. x-y+z-2=0\ a n d\ 3x+2y-z+4=0

If x+y+z=0 prove that |a x b y c z c y a z b x b z c x a y|=x y z|a b cc a bb c a|

The equation of the plane through intersectioof planes x=2y+3z=4 and 2x+y-z=-5 and perpendicular to the plane 5x+3y+6z+8=0 is (A) 7x-2y+3x+81=0 (B) 23x+14y-9z+48=0 (C) 51x+15y+50z+173=0 (D) none of these

Find the equation of the plane through the line of intersection of the planes x+2y+3z+2=0 , 2x+3y-z+3=0 and perpendicular to the plane x+y+z=0