Then equation of OD and BG are \[\frac{x}{a}=\frac{y}{a}=\frac{z}{a}\] and \[\frac{x}{a}=\frac{y-a}{-a}=\frac{z}{a}\] respectively.
Hence, angle between OD and BG is
\[{{\cos }^{-1}}\left( \frac{{{a}^{2}}-{{a}^{2}}+{{a}^{2}}}{\sqrt{3{{a}^{2}}}.\,\sqrt{3{{a}^{2}}}} \right)={{\cos }^{-1}}\,\left( \frac{1}{3} \right)\]. Note: Students should remember this question as a fact.