Walker, Halliday & Resnick — Vectors: Problem 34

34 Two vectors are presented as \( \vec{a} = 3.0\hat{i} + 5.0\hat{j} \) 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 \( \vec{b} \). (Hint: For (d), consider Eq. 3-20 and Fig. 3-18.)