Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Questions to Guide Your Review - Page 733: 3


Explanation given below.

Work Step by Step

We write the vector in component form. ${\bf u}$=$\langle u_{1}, u_{2}, u_{3}\rangle\qquad $ or $\langle u_{1}, u_{2}\rangle$, if in two dimensions The magnitude of the vector is its length, $|{\bf u}|=\sqrt{u_{1}^{2}+u_{2}^{2}+u_{3}^{2}}$ and the direction of the vector is the unit vector (vector of magnitude 1, in the direction of ${\bf u}$): $\displaystyle \frac{{\bf u}}{|{\bf u}|}=\frac{1}{\sqrt{u_{1}^{2}+u_{2}^{2}+u_{3}^{2}}}\cdot\langle u_{1}, u_{2}, u_{3}\rangle$
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