Halliday, Resnick & Walker — Vectors: Problem 17

17 Three vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) each have a magnitude of \(50 \text{ m}\) and lie in an \(xy\) plane. Their directions relative to the positive direction of the \(x\) axis are \(30^\circ\), \(195^\circ\), and \(315^\circ\), respectively. What are (a) the magnitude and (b) the angle of the vector \(\vec{a} + \vec{b} + \vec{c}\), and (c) the magnitude and (d) the angle of the vector \(\vec{a} - \vec{b} + \vec{c}\)? What are the (e) magnitude and (f) angle of a fourth vector \(\vec{d}\) such that \((\vec{a} + \vec{b}) - (\vec{c} + \vec{d}) = 0\)?