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Prove that the sum of three vectors d...

Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.

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Three coinitial vectors of magnitudes a, 2a and 3a meet at a point and their directions are along the diagonals if three adjacent faces if a cube. Determined their resultant R. Also prove that the sum of the three vectors determinate by the diagonals of three adjacent faces of a cube passing through the same corner, the vectors being directed from the corner, is twice the vector determined by the diagonal of the cube.

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Prove by vector method that the medians of a triangle are concurrent.