Halliday, Resnick & Walker — Vectors: Problem 74

Vector \(\vec{a}\) lies in the \(yz\) plane \(63.0^\circ\) from the positive direction of the \(y\) axis, has a positive \(z\) component, and has magnitude \(3.20\) units. Vector \(\vec{b}\) lies in the \(xz\) plane \(48.0^\circ\) from the positive direction of the \(x\) axis, has a positive \(z\) component, and has magnitude \(1.40\) units. Find (a) \(\vec{a} \cdot \vec{b}\), (b) \(\vec{a} \times \vec{b}\), and (c) the angle between \(\vec{a}\) and \(\vec{b}\).