Halliday, Resnick & Walker — Vectors: Problem 73

Two vectors are given by \(\vec{a} = 3.0\hat{i} + 5.0\hat{j}\) and \(\vec{b} = 2.0\hat{i} + 4.0\hat{j}\). Find (a) \(\vec{a} \times \vec{b}\), (b) \(\vec{a} \cdot \vec{b}\), (c) \((\vec{a} + \vec{b}) \cdot \vec{b}\), and (d) the component of \(\vec{a}\) along the direction of \(\vec{b}\).