5.1.9 Affine transformations

Problem: Find the square of the distance from the point \( A= \) \( (2,0,1,2) \) to the plane \[ P:\left(\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \\ x_{4} \end{array}\right)=\left(\begin{array}{l} 1 \\ 1 \\ 2 \\ 2 \end{array}\right)+t_{1}\left(\begin{array}{l} 1 \\ 0 \\ 0 \\ 1 \end{array}\right)+t_{2}\left(\begin{array}{l} 0 \\ 1 \\ 0 \\ 1 \end{array}\right)+t_{3}\left(\begin{array}{l} 0 \\ 0 \\ 1 \\ 1 \end{array}\right) . \]