Halliday, Resnick & Walker — Vectors: Problem 45

Vectors \(\vec{A}\) and \(\vec{B}\) lie in an \(xy\) plane. \(\vec{A}\) has magnitude 8.00 and angle \(130^\circ\); \(\vec{B}\) has components \(B_x = -7.72\) and \(B_y = -9.20\). (a) What is \(5\vec{A} \cdot \vec{B}\)? What is \(4\vec{A} \times 3\vec{B}\) in (b) unit-vector notation and (c) magnitude-angle notation with spherical coordinates (see Fig. 3.14)? (d) What is the angle between the directions of \(\vec{A}\) and \(4\vec{A} \times 3\vec{B}\)? (Hint: Think a bit before you resort to a calculation.) What is \(\vec{A} + 3.00\hat{k}\) in (e) unit-vector notation and (f) magnitude-angle notation with spherical coordinates?