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 - Section 12.2 - Vectors - Exercises 12.2 - Page 704: 6

Answer

$\lt -16,29\gt$ and $\sqrt {1097}$

Work Step by Step

The magnitude of a vector is:$|n|=\sqrt{n_1^2+n_2^2}$ Here, $u=\lt 3,-2 \gt; v= \lt -2,5 \gt$ Now, $-2u +5v=-2\lt 3,-2 \gt +5 \lt -2,5 \gt =\lt -16,29 \gt$ and $|\lt -16,29\gt|=\sqrt{(-16)^2+(29)^2}=\sqrt {1097}$ Hence, we have $\lt -16,29\gt$ and $\sqrt {1097}$
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