Find the orthocenter

Geometry Level 5

In the Cartesian plane, we have a triangle \(ABC\) where \(A,B,C\) whose coordinates are \((1,2,3) , (5,3,1) , (3,4,5)\), respectively.

If the coordinate of the orthocenter of the triangle \(ABC\) is \((x,y,z)\), find \(2({x}^{2}+{y}^{2}+{z}^{2}) \).

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