Compute the angle between \( \vec{i}+\vec{j}+\vec{k} \) and \( \vec{i}-\vec{j}-\vec{k} \). Leave your answer in exact form.

5th Ed: #17

\( \theta = \cos ^{-1} \left ( \frac{1-1-1}{\sqrt{1+1+1}\sqrt{1+1+1}} \right ) = \cos^{-1} \left ( \frac{-1}{3} \right ) \)