Mathematics

Problem

Let

\mathbf{a}

\mathbf{b}

and

\mathbf{c}

be the position vectors of the vertices

A

B

and

C

of a triangle. a. (i) Show that the midpoint

M

BC

has position vector

\dfrac{\mathbf{b}+\mathbf{c}}{2}

. b. (ii) Prove that the centroid

G

\triangle ABC

has position vector

\dfrac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{3}

. c. (iii) Hence deduce that the centroid divides each median internally in the ratio

2:1