Two vectors A and B are given by A= 5i + 6j + 7k and B= 3i - 8j +2k. If these two vectors are drawn starting at the same point, whatis the angle between the two vectors?

Calculate the dot product of the two vectors using two different techniques:


\vec A \cdot \vec B = |A||B| \cos \theta \\
\vec A \cdot \vec B = a_i b_i + a_j b_j + a_k b_k


Set them equal, and solve for \theta