Question

The sum of the three vectors determined by the medians of a triangle directed from the vertices is

• A. $0$
• B. $1$
• C. $-1$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $0$

$\because D$ is middle point of $BC$

$\therefore AD=\frac{AB+AC}{2}$ ...(1)

$E$ is middle point of $CA$

$\therefore BE=\frac{BA+BC}{2}$ ....(2)

$F$ is middle point of $AB$

$\therefore CF=\frac{CB+CA}{2}$ ...(3)

Adding (1),(2) and (3), we get

$AD+BE+CF=0$