Halliday, Resnick & Walker — Vectors: Problem 23

23 If \(\vec{b} = (3.0)\hat{i} + (4.0)\hat{j}\) and \(\vec{a} = \hat{i} - \hat{j}\), what is the vector having the same magnitude as that of \(\vec{b}\) and parallel to \(\vec{a}\)? Correction based on standard notation in context: The text in the problem description area of the screenshot shows: "If \(\vec{b} = (3.0)\hat{i} + (4.0)\hat{j}\) and \(\vec{a} = \hat{i} - \hat{j}\)...". However, the OCR and typical problem sets usually list \(\vec{a}\) first. Looking closely at the screenshot for Problem 23: "If \(\vec{b} = (3.0)\hat{i} + (4.0)\hat{j}\) and \(\vec{a} = \hat{i} - \hat{j}\), what is the vector having the same magnitude as that of \(\vec{b}\) and parallel to \(\vec{a}\)?". I will solve exactly as written in the text.