Halliday, Resnick & Walker — Vectors: Problem 30

30 Here are two vectors: \(\vec{a} = (4.0\text{ m})\hat{i} - (3.0\text{ m})\hat{j}\) and \(\vec{b} = (6.0\text{ m})\hat{i} + (8.0\text{ m})\hat{j}\). What are (a) the magnitude and (b) the angle (relative to \(\hat{i}\)) of \(\vec{a}\)? What are (c) the magnitude and (d) the angle of \(\vec{b}\)? What are (e) the magnitude and (f) the angle of \(\vec{a} + \vec{b}\); (g) the magnitude and (h) the angle of \(\vec{b} - \vec{a}\); and (i) the magnitude and (j) the angle of \(\vec{a} - \vec{b}\)? (k) What is the angle between the directions of \(\vec{b} - \vec{a}\) and \(\vec{a} - \vec{b}\)?