1. ## Pyramid problem

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 vectors u,v,w are equals.
I need to prove that $\displaystyle {\overrightarrow{SM} }$ is perpendicular to the plane of the base ABC.

2. ## Re: Pyramid problem

Originally Posted by xbox360
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 vectors u,v,w are equals.
I need to prove that $\displaystyle {\overrightarrow{SM} }$ is perpendicular to the plane of the base ABC.
Hint:$\vec{AB} =v - u$. What do you get when you dot that into $\vec{SM}$? And similarly for the other two sides of the base.