Halliday, Resnick & Walker — Vectors: Problem 84

Jungle gym, cross products, unit vectors. 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 steps. For each step, the distance (in meters) and direction in which you move are given by the cross product \(\vec{A} \times \vec{B}\) of the given vectors \(\vec{A}\) and \(\vec{B}\). For example, the first move is 18 m in the +z direction. What is the magnitude \(d_{\text{net}}\) of your final displacement from the origin? (a) \(\vec{A} = 3.0\hat{i}, \vec{B} = 6.0\hat{j}\) (b) \(\vec{A} = -4.0\hat{i}, \vec{B} = 3.0\hat{k}\) (c) \(\vec{A} = 2.0\hat{j}, \vec{B} = 4.0\hat{k}\) (d) \(\vec{A} = 3.0\hat{j}, \vec{B} = -8.0\hat{j}\) (e) \(\vec{A} = 4.0\hat{k}, \vec{B} = -2.0\hat{i}\) (f) \(\vec{A} = 2.0\hat{i}, \vec{B} = -4.0\hat{j}\)