Let P$1,$ P$2$ and P$3$ be points relative to a fixed origin O and let r$1,$ r$2$ and r$3$ be the $[5]$

respective position vectors from O to each point. Suppose the vector equation:

$\backslash$alpha r$1+\backslash$beta r$2+\backslash$gamma r$3=0$

holds with respect to O$.$ Show that it holds with respect to any other origin O$0$

if

and only if $\backslash$alpha $+\backslash$beta $+\backslash$gamma $=0.$