Halliday, Resnick & Walker — Vectors: Problem 59

\(\vec{A}\) has the magnitude \(12.0\text{ m}\) and is angled \(60.0^\circ\) counterclockwise from the positive direction of the \(x\) axis of an \(xy\) coordinate system. Also, \(\vec{B} = (12.0\text{ m})\hat{i} + (8.00\text{ m})\hat{j}\) on that same coordinate system. We now rotate the system counterclockwise about the origin by \(20.0^\circ\) to form an \(x'y'\) system. On this new system, what are (a) \(\vec{A}\) and (b) \(\vec{B}\), both in unit-vector notation?