Question

Show that the equation ax+ by+ 6= 0, by+ cz+ p= 0,cz+ax+q=0 represent plane representing perpendicular to xy,yz,zx planes

Answer 1

i, j , k are unit vectors in x, y, z directions.

PL1: a x + b y + 6 = 0,  Normal N1:  a i + b j    is in the x-y plane.  So PL1 is perpendicular to the x-y plane.

PL2: b y + c z + p = 0,  Normal N2:  b j + c k   is in the y-z plane.  So PL2 is perpendicular to y-z plane.

PL3: c z + a x + q = 0,  Normal N3:  c k + a i  is in the z-x plane. So PL3 is perpendicular to z-x plane.