Prove that the altitudes of a triangle are concurrent.

Explanation

Let triangle {ABC} be a triangle and let {AD}, {BE} be its to altitudes intersecting at O.

In order to prove that the altitudes are concurrent. it is sufficient to prove that {CO} is perpendicular to {AB}.

Taking O as the origin, let the position vectors of A, B, C be vec{a}, vec{b}, vec{c} respectively.

Then, `vec{{O} A}=vec{{a}} ; {OB}=vec{{b}} ; {OC}=vec{c}`

Now {AD} perp {BC}
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Rightarrow vec{{O}} {A} perp vec{{B}} {C}`
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