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atjari
Please someone help me to do the second part of the question below. If O is any point within triangle ABC and P, Q, R are midpoints of the sides AB, BC, CA respectively. i)Prove that vectorOA+vectorOB+vectorOC=vectorOP+vectorOQ+vectorOR ii)Does the result hold if O is any point outside the triangle? Prove your result.
Assume O to be the center ... now you have OP + OQ + OR = (OC + CP) + (OA + AQ) + (OB + BR) .. Vector addition Hence = (OC+ OA + OB) + (CP + AQ + BR) = (OC + OA + OB) + 0.5*(CB + AC + BA) Now CB + AC+ BA = 0 (it forms a triangle). Hence = OC + OA + OB.. hence proved 2) Just workout the same equation from outside the triangle to find...
you mean that there is no difference even the point is outside the triangle.
Yes it won't make any difference..