Two flat plates are parallel, and they lie in the planes 2x - 2y + z = 8 and 2x - 2y + z = -4, with…

Step 1. The distance. $2 - 4 + 1 - 8 = -9$. The length of the normal is $\sqrt{4 + 4 + 1} = 3$, so the distance is $\dfrac{9}{3} = 3$ metres.

Step 2. The foot. $F = P - \dfrac{-9}{9}\,(2, -2, 1) = (1, 2, 1) + (2, -2, 1) = (3, 0, 2)$. Check: $6 - 0 + 2 = 8$.

Step 3. The plates. The coefficients are the same. The distance is $\dfrac{\lvert 8 - (-4) \rvert}{3} = 4$ metres.