Serway & Jewett — Vectors: Problem 20

Given the displacement vectors \(\vec{A} = (3\hat{i} - 4\hat{j} + 4\hat{k}) \text{ m}\) and \(\vec{B} = (2\hat{i} + 3\hat{j} - 7\hat{k}) \text{ m}\), find the magnitudes of the following vectors and express each in terms of its rectangular components. (a) \(\vec{C} = \vec{A} + \vec{B}\) (b) \(\vec{D} = 2\vec{A} - \vec{B}\)