Question

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.

Answer 1

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...

Answer 2

you mean that there is no difference even the point is outside the triangle.

Answer 3

Shaan pls help

Answer 4

Yes it won't make any difference..

Answer 5

Thanx a lot.