Walker, Halliday & Resnick — Vectors: Problem 41

41 Use the definition of scalar product, \(\vec{a} \cdot \vec{b} = ab \cos \theta\), and the fact that \(\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y + a_z b_z\) to calculate the angle between the following two vectors: \(\vec{a} = 4.0\hat{i} + 4.0\hat{j} + 4.0\hat{k}\) and \(\vec{b} = 3.0\hat{i} + 2.0\hat{j} + 4.0\hat{k}\).