Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 7 - Section 7.5 - Vectors: An Algebraic Approach - 7.5 Problem Set - Page 405: 42

Answer

\begin{align*} U+V&=(2,-7)\\ U-V&=(2,7)\\ 2U-3V&=(4,21). \end{align*}

Work Step by Step

We have $U=\langle 2,0\rangle, V=\langle 0,-7\rangle.$ First find $U+V$, \begin{align*} U+V&=(2,0)+(0,-7)\\ &=(2+0,0-7)\\ &=(2,-7). \end{align*} Hence, $U+V=(2,-7).$ Then find $U-V$, \begin{align*} U-V&=(2,0)-(0,-7)\\ &=(2-0,0-(-7))\\ &=(2,7). \end{align*} Hence, $U-V=(2,7).$ In the end find, \begin{align*} 2U-3V&=2(2,0)-3(0,-7)\\ &=(4,0)-(0,-21)\\ &=(4-0,0+21)\\ &=(4,21). \end{align*}
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