I tryed to solve an apearently simple geometry problem but i could not. Someone please help me!(excuse my english)

In the interior of an equilateral triangle (whose center is O) we consider a point P and let P1, P2, P3 be the orthogonal projection of the point P on the three sides of the triangle. prove that $\displaystyle \vec{PP_1}+\vec{PP_2}+\vec{PP_3}=\frac{3}{2}\vec{P O}$