Mathematics · Vector Algebra

Let the position vectors of the vertices of a triangle ABC be vector a, vector b, and vector c. If on the plane of the triangle, P is a point having position vector x such that vector x · (vector c - vector b) = vector a · vector c - vector a · vector b and vector x · (vector a - vector c) = vector a · vector b - vector b · vector c, then for the triangle ABC, P is the: