# 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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