Gọi \(I\left(x;y;z\right)\) là điểm thỏa mãn \(\overrightarrow{IA}-\overrightarrow{IB}+\overrightarrow{IC}=0\)
\(\left\{{}\begin{matrix}\overrightarrow{IA}=\left(1-x;-2-y;1-z\right)\\\overrightarrow{IB}=\left(-x;2-y;-1-z\right)\\\overrightarrow{IC}=\left(2-x;-3-y;1-z\right)\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}3-x=0\\-7-y=0\\3-z=0\end{matrix}\right.\) \(\Rightarrow I\left(3;-7;3\right)\)
\(MA^2-MB^2+MC^2=\left(\overrightarrow{MI}+\overrightarrow{IA}\right)^2-\left(\overrightarrow{MI}+\overrightarrow{IB}\right)^2+\left(\overrightarrow{MI}+\overrightarrow{IC}\right)^2\)
\(=MI^2+IA^2+IB^2+IC^2\ge IA^2+IB^2+IC^2\)
Dấu "=" xảy ra khi M trùng I hay \(M\left(3;-7;3\right)\)
\(\Rightarrow P=134\)
