\magnification=1200 \hsize=4in \overfullrule=0pt \input amssym %\def\frac#1 #2 {{#1\over #2}} \def\emph#1{{\it #1}} \def\em{\it} \nopagenumbers \noindent % % {\bf Alex Iosevich and Steven Senger} % % \medskip \noindent % % {\bf Orthogonal Systems in Vector Spaces over Finite Fields} % % \vskip 5mm \noindent % % % % We prove that if a subset of the $d$-dimensional vector space over a finite field is large enough, then it contains many $k$-tuples of mutually orthogonal vectors. \bye .