Một cơ sở trực giao của R3 là:

\[\left\{ {\left( {1,1,0} \right),\left( { - 1,1,1} \right),\left( { - 1,0,1} \right)} \right\}\]

\[\left\{ {\left( {1,1,0} \right),\left( { - \sqrt 2 ,\sqrt 2 ,0} \right),\left( {0,0, - 1} \right)} \right\}\]

\[\left\{ {\left( {1,1,0} \right),\left( {0,1,0} \right),\left( {1,0,1} \right)} \right\}\]

\[\left\{ {\left( {0,1,0} \right),\left( {1, - 1,0} \right),\left( { - 1,0,1} \right)} \right\}\]