Serway & Jewett — Vectors: Problem 19

The vector \(\vec{A}\) has \(x\), \(y\), and \(z\) components of 8.00, 12.0, and -4.00 units, respectively. (a) Write a vector expression for \(\vec{A}\) in unit-vector notation. (b) Obtain a unit-vector expression for a vector \(\vec{B}\) one-fourth the length of \(\vec{A}\) pointing in the same direction as \(\vec{A}\). (c) Obtain a unit-vector expression for a vector \(\vec{C}\) three times the length of \(\vec{A}\) pointing in the direction opposite the direction of \(\vec{A}\).