In coordinate space, $A = (1,2,3),$ $B = (5,3,1),$ and $C = (3,4,5).$  Find the orthocenter of triangle $ABC.$
Question:
In coordinate space, $A = (1,2,3),$ $B = (5,3,1),$ and $C = (3,4,5).$  Find the orthocenter of triangle $ABC.$
Answer:
Let's think step by step.

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\left( \frac{5}{2}, 3, \frac{7}{2} \right)
In coordinate space, $A = (1,2,3),$ $B = (5,3,1),$ and $C = (3,4,5).$  Find the orthocenter of triangle $ABC.$
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