Interior product (contraction) symbol

I stumbled upon the correct markup used in Wikipedia's article on geometric algebra. I looked at the code and found the symbol is given by \lrcorner. \llcorner is the same thing but flipped horizontally.

You can import the symbol from MnSymbol by saying

\DeclareFontFamily{U}{MnSymbolC}{}
\DeclareSymbolFont{MnSyC}{U}{MnSymbolC}{m}{n}
\DeclareFontShape{U}{MnSymbolC}{m}{n}{
    <-6>  MnSymbolC5
   <6-7>  MnSymbolC6
   <7-8>  MnSymbolC7
   <8-9>  MnSymbolC8
   <9-10> MnSymbolC9
  <10-12> MnSymbolC10
  <12->   MnSymbolC12}{}
\DeclareMathSymbol{\intprod}{\mathbin}{MnSyC}{'270}

This way you won't override your math fonts with MnSymbol.

The alternative way with reversing the \lnot symbol is

\usepackage{graphicx}
\newcommand{\intprod}{\mathbin{\raisebox{\depth}{\scalebox{1}[-1]{$\lnot$}}}}

If the symbol is needed also in other sizes, then

\newcommand{\intprod}{\mathbin{\mathpalette\dointprod\relax}}
\newcommand{\dointprod}[2]{%
  \raisebox{\depth}{\scalebox{1}[-1]{$#1\lnot$}}}

Here's a picture of the output in the two ways.