Halliday, Resnick & Walker — Vectors: Problem 81

Orienteering. In an orienteering class, you have the goal of moving as far (straight-line distance) from base camp as possible by making three straight-line moves. You may use the following displacements in any order: (a) \(\vec{a}\), 2.0 km due east (directly toward the east); (b) \(\vec{b}\), 2.0 km 30° north of east (at an angle of 30° toward the north from due east); (c) \(\vec{c}\), 1.0 km due west. Alternately, you may substitute either \(-\vec{b}\) for \(\vec{b}\) or \(-\vec{c}\) for \(\vec{c}\). What is the greatest distance you can be from base camp at the end of the third displacement (regardless of direction)?