Vectors in geometry

Question

How can one use vectors to solve problems in geometry like this one ?

Prove that the perpendicular bisectors of the sides of a triangle meet at a point.

Any good book recommendations are welcomed.

Answer 1

Being in India, I would strongly recommend reading Vectors and Geometry by G S Pandey and R R Sharma. It has very good examples and a strong problem set. It also has a very in-depth approach to basic concepts of geometry using vectors.

As for the question you posed, this has already been answered on MSE.

Answer 2

Perpendicular bisectors at one side represent the loci of the points at equal distance from the two vertex of that side, thus the three perpendicular bisectors have to meet each other at the center of the triangle's circumcircle, denoted as circumcenter.