University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 11 - Practice Exercises - Page 639: 53

Answer

$ \lt \dfrac{10}{\sqrt{35}},\dfrac{-2}{\sqrt{35}},\dfrac{-6}{\sqrt{35}} \gt$

Work Step by Step

Here, $|v|=\sqrt{(5)^2+(-1)^2+(-3)^2}=\sqrt {35}$ The unit vector $\hat{\textbf{u}}$ can be calculated as: $\hat{\textbf{u}}=\dfrac{v}{|v|}$ Now, $2 \hat{\textbf{u}}=2 [\dfrac{\lt 5,-1,-3 \gt}{\sqrt {35}}]= \lt \dfrac{10}{\sqrt{35}},\dfrac{-2}{\sqrt{35}},\dfrac{-6}{\sqrt{35}} \gt$ Thus, our final answer is: $ \lt \dfrac{10}{\sqrt{35}},\dfrac{-2}{\sqrt{35}},\dfrac{-6}{\sqrt{35}} \gt$
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