PQR is a triangle. A is a vector which has the same magnitude as PQ and is perpendicular to PQ pointing outward from the triangle PQR. B is perpendicular to QR and has the same magnitude as QR again pointing outward from PQR. Same for C with RP. How do you prove that vectors A + B + C = 0?

Note: I have to use dot products and the fact that vectors PQ + QR + RP = 0. I am trying to work out 2 vectors version and still haven't got a convincing proof for 2 vector version only using vectors. (2 vector version: S and T are two vectors such that S + T = 0. U is perpendicular to S counterclockwise from S and has the same magnitude as S. Same for T and V. Prove that U + V = 0.)

Question

PQR is a triangle. A is a vector which has the same magnitude as PQ and is perpendicular to PQ pointing outward from the triangle PQR. B is perpendicular to QR and has the same magnitude as QR again pointing outward from PQR. Same for C with RP. How do you prove that vectors A + B + C = 0?

Note: I have to use dot products and the fact that vectors PQ + QR + RP = 0. I am trying to work out 2 vectors version and still haven't got a convincing proof for 2 vector version only using vectors. (2 vector version: S and T are two vectors such that S + T = 0. U is perpendicular to S counterclockwise from S and has the same magnitude as S. Same for T and V. Prove that U + V = 0.)

irishboy123 · Answer

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