Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 7 - Applications of Trigonometry and Vectors - Section 7.4 Vectors, Operations, and the Dot Product - 7.4 Exercises - Page 329: 24

Answer

(a) $\langle 4,4 \rangle$ (b) $\langle 12,-12\rangle$ (c) $\langle -8,4 \rangle$

Work Step by Step

First, we find the vector notations of both $\textbf{u}$ and $\textbf{v}$. Upon observation, we find that $\textbf{u}=\langle 8,-4 \rangle$ and $\textbf{v}=\langle -4,8 \rangle$. (a) To find the value of $\textbf{u}+\textbf{v}$, we substitute the vectors $\textbf{u}$ and $\textbf{v}$ in the expression and simplify: $\textbf{u}+\textbf{v}$ $=\langle 8,-4 \rangle+\langle -4,8 \rangle$ $=\langle 8-4,-4+8\rangle$ $=\langle 4,4 \rangle$ (b) To find the value of $\textbf{u}-\textbf{v}$, we substitute the vectors $\textbf{u}$ and $\textbf{v}$ in the expression and simplify: $\textbf{u}-\textbf{v}$ $=\langle 8,-4 \rangle-\langle -4,8 \rangle$ $=\langle 8-(-4),-4-8\rangle$ $=\langle 12,-12\rangle$ (c) To find the value of $-\textbf{u}$, we substitute the vector $\textbf{u}$ in the expression and simplify: $-\textbf{u}$ $=-\langle 8,-4 \rangle$ $=\langle -1(8),-1(-4) \rangle$ $=\langle -8,4 \rangle$
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