Serway & Jewett — Vectors: Problem 23

(a) Taking \(\vec{A} = (6.00 \hat{i} - 8.00 \hat{j})\) units, \(\vec{B} = (-8.00 \hat{i} + 3.00 \hat{j})\) units, and \(\vec{C} = (26.0 \hat{i} + 19.0 \hat{j})\) units, determine \(a\) and \(b\) such that \(a \vec{A} + b \vec{B} + \vec{C} = 0\). (b) A student has learned that a single equation cannot be solved to determine values for more than one unknown in it. How would you explain to him that both \(a\) and \(b\) can be determined from the single equation used in part (a)?