. . Application of dot and cross products in Geometry Example . (Apollonius's theorem) If D is the midpoint of the side BC of a triangle ABC , show by vector method that (| | ) AB AC AD BD Let A be the origin, b be the position vector of B and c be the position vector of C .
Now D is the midpoint of BC , and so the, position vector of D is . Therefore, we have Fig. . Fig.