Three vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) each have a magnitude of 53.0 m and lie in an xy plane. Their directions relative to the positive direction of the x axis are 35.0\(^{\circ}\), 190\(^{\circ}\), and 314\(^{\circ}\), respectively. What are (a) the magnitude and (b) the angle of the vector \(\vec{a} + \vec{b} + \vec{c}\) relative to the +x direction in the range of (-180\(^{\circ}\), 180\(^{\circ}\)), and (c) the magnitude and (d) the angle of \(\vec{a} - \vec{b} + \vec{c}\) in the range of (-180\(^{\circ}\), 180\(^{\circ}\)? What are (e) the magnitude and (f) the angle (in the range of (-180\(^{\circ}\), 180\(^{\circ}\))) of a fourth vector \(\vec{d}\) such that \((\vec{a} + \vec{b}) - (\vec{c} + \vec{d}) = \vec{0}\)?