Trigonometry/Some theorems using vectors

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Some theorems using vectors.

Circumcentre and orthocentre[edit]

For a triangle ABC, let the circumcentre be O and the orthocentre be H. Then the vector sum of OA, OB and OC is OH.

Centroid[edit]

For a triangle ABC, let the centroid be G. Then the vector sum of GA, GB and GC is 0.