Halliday, Resnick & Walker — Vectors: Problem 86

Jungle gym, cross products, magnitude-angle. A coordinate system is laid out along the bars of a large 3D jungle gym (Fig. 3.20). You start at the origin and then move according to the following instructions. The direction for each move is explicitly shown but the distance (in meters) you move in that direction must be determined by evaluating the cross product \(\vec{A} \times \vec{B}\) of vectors \(\vec{A}\) and \(\vec{B}\) with the given magnitudes and separation angle \(\theta\). For example, the first move is 12 m in the \(+y\) direction. What is the magnitude \(d_{net}\) of your final displacement from the origin? (a) \(+y, A = 3.0, B = 4.0, \theta = 90^\circ\) (b) \(-z, A = 3.0, B = 2.0, \theta = 30^\circ\) (c) \(-y, A = 6.0, B = 8.0, \theta = 0^\circ\) (d) \(+x, A = 4.0, B = 5.0, \theta = 150^\circ\) (e) \(-y, A = 7.0, B = 2.0, \theta = 30^\circ\) (f) \(-x, A = 4.0, B = 3.0, \theta = 90^\circ\)