I have the points O,A,B and C.Relative to O, the position vectors of A, B and C are (1,4,2), (3,3,3), (2,−1,1)Want to show that the lines OB and AC bisect each other.Is it sufficient to show that 1 2 O B → = O A → + 1 2 A C → ?Are there other ways using vectors?

Question

I have the points O,A,B and C.Relative to O, the position vectors of A, B and C are (1,4,2), (3,3,3), (2,−1,1)Want to show that the lines OB and AC bisect each other.Is it sufficient to show that       1    2                      O        B            →        =                    O        A            →        +      1    2                      A        C            →      ?Are there other ways using vectors?

salumeqi · Accepted Answer

Yes, your method is correct.You may also show that                    O        A            →        =                    C        B            →      and                    O        C            →        =                    A        B            →      which make the quadrilateral OABC into a parallelogram where the diagonals bisect each other.