Halliday, Resnick & Walker — Vectors: Problem 9

Two vectors are given by \[ \vec{a} = (4.0 \text{ m})\hat{i} - (3.0 \text{ m})\hat{j} + (1.0 \text{ m})\hat{k} \] and \[ \vec{b} = (-1.0 \text{ m})\hat{i} + (1.0 \text{ m})\hat{j} + (4.0 \text{ m})\hat{k} \] In unit-vector notation, find (a) \( \vec{a} + \vec{b} \), (b) \( \vec{a} - \vec{b} \), and (c) a third vector \( \vec{c} \) such that \( \vec{a} - \vec{b} + \vec{c} = 0 \).