We have ABCABC a scalene triangle, and a point MM in plane of this triangle. How to prove that vec(AB)*vec(CM)+vec(AC)*vec(MB)+vec(AM)*vec(BC) = 0−−→AB⋅−−→CM+−−→AC⋅−−→MB+−−→AM⋅−−→BC=0?
2 Answers
Please see the proof below
Explanation:
Apply Chasles' Relation
But,
Therefore, Adding the first
We have
Now by triangle law we have
For
For
For
Now using [1] we get