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I tried doing a search for this one here, but I didn't seem to come up with much...

## Homework Statement

Prove that the three altitudes of a triangle meet at one point.

## Homework Equations

Well, I am not really sure, but I know that Ceva's theorem might help me prove this, but I want to prove it vectorally, so I don't know if it will be much help at all.

## The Attempt at a Solution

My instructor gave a hint for this proof by saying, show each of the triangles cevians are perpandicular to its opposite side... I can see pictorally this is ok, but where to start...???

Thanks