Recover plane-distance and coupled-motion parameters
\[\Pi:\ x+2y+2z=-3,\qquad P(\lambda)=\begin{pmatrix}-1\\-1\\1\end{pmatrix}+\lambda\begin{pmatrix}3\\0\\0\end{pmatrix}\]
Find every real λ for which the perpendicular distance from P(λ) to Π equals 4. Give the distinct count and ordered extreme values L≤U; if there is one value, enter it in both fields. Then find the perpendicular foot H on Π from P(L)