anonymous
  • anonymous
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.
Mathematics
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anonymous
  • anonymous
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.
Mathematics
chestercat
  • chestercat
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
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...
anonymous
  • anonymous
you mean that there is no difference even the point is outside the triangle.
anonymous
  • anonymous
Shaan pls help

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anonymous
  • anonymous
Yes it won't make any difference..
anonymous
  • anonymous
Thanx a lot.

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