Hi, I have this problem:

given pyramid SABC that the base is ABC, and the apex is S.

u,v,w,are vectors with the same size.

Consider M is a dot in the base so $\displaystyle {\overrightarrow{SM}=\frac{\bf{u}}{3}+\frac{\bf{v} }{3}+\frac{\bf{w}}{3}}$,

and also, all the angles between the vectorsu,v,ware equals.

I need to prove that $\displaystyle {\overrightarrow{SM} } $ is perpendicular to the plane of the base ABC.