Halliday, Resnick & Walker — Vectors: Problem 83

Jungle gym, dot 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 instructions. The direction for each move is explicitly shown but the distance (in meters) you move in that direction must be determined by evaluating a dot product of the given vectors \(\vec{A}\) and \(\vec{B}\). For example, the first move is 21 m in the \(-x\) direction. What is the magnitude \(d_{net}\) of your final displacement from the origin? (a) \(-x\), \(\vec{A} = 3.0\hat{i}\), \(\vec{B} = 7.0\hat{i}\) (b) \(-z\), \(\vec{A} = 2.0\hat{k}\), \(\vec{B} = 3.0\hat{j}\) (c) \(+y\), \(\vec{A} = 5.0\hat{j}\), \(\vec{B} = 3.0\hat{j}\) (d) \(+x\), \(\vec{A} = 7.0\hat{k}\), \(\vec{B} = 2.0\hat{k}\) (e) \(-z\), \(\vec{A} = 3.0\hat{i}\), \(\vec{B} = 2.0\hat{i}\) (f) \(-y\), \(\vec{A} = 3.0\hat{i}\), \(\vec{B} = 7.0\hat{j}\)