Halliday, Resnick & Walker — Vectors: Problem 42

42 In a meeting of mimes, mime 1 goes through a displacement \(\vec{d}_1 = (4.0\text{ m})\hat{i} + (5.0\text{ m})\hat{j}\) and mime 2 goes through a displacement \(\vec{d}_2 = (-3.0\text{ m})\hat{i} + (4.0\text{ m})\hat{j}\). What are (a) \(\vec{d}_1 \cdot \vec{d}_2\), (b) \(\vec{d}_1 \times \vec{d}_2\), (c) \((\vec{d}_1 + \vec{d}_2) \cdot \vec{d}_2\), and (d) the component of \(\vec{d}_1\) along the direction of \(\vec{d}_2\)? (Hint: For (d), see Eq. 3-20 and Fig. 3-18.)