University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 11 - Section 11.2 - Vectors - Exercises - Page 608: 28



Work Step by Step

Here, $v=\dfrac{3}{5}i+\dfrac{4}{5}k$ and $|v|=\sqrt{(\dfrac{3}{5})^2+(\dfrac{4}{5})^2}=\sqrt {\dfrac{25}{25}}=1$ The unit vector $\hat{\textbf{v}}$ can be calculated as: $\hat{\textbf{v}}=\dfrac{v}{|v|}$ Now, $\hat{\textbf{v}}=\dfrac{(\dfrac{3}{5}i+\dfrac{4}{5}k)}{1}=(\dfrac{3}{5}i+\dfrac{4}{5}k)$ Thus, $v=|v|\hat{\textbf{v}}=1(\dfrac{3}{5}i+\dfrac{4}{5}k)$
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