Consider the planes with equations 2x+4y-4z=1 and x+2y-2z=-3. Explain why these planes are parallel.Find the distance between the planes Solution The planes are parallel because the left sides are functionally the same. Multiply all the second by 2 and we get 2x+4y-4z=-6. If two planes never intersect they are parallel. To find the distance use: D=|Ax1+By1+Cz1+D|/sqrt(a^2+b^2+c^2) let\'s use the point -3, 0, 0 on the second plane. So D=|2*-3+0+0-1|/sqrt(2^2+4^2+4^2) or 7/6..