Prove that angle bisectors of a triangle are concurrent using vectors. Also, find the position vector of the point of concurrency in terms of position vectors of the vertices.
I solved this without using vectors to get some idea. I am not sure how to prove it using vectors. I don't want to use vector equations for straight lines and then find the point of concurrency. That's like solving using coordinate geometry.
Let represent the sides respectively.
The angle bisectors are along
Let the sides be . Let be one of the angular bisector.
Hence
What should be the next step? Or is there a better method?