Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 8 - Application of Trigonometry - 8.4 Algebraically Defined Vectors and the Dot Product - 8.4 Exercises - Page 790: 60

Answer

$-24$

Work Step by Step

Our aims is to compute the dot product , for this we will multiply the corresponding components together and then add. In general, we have the formula as: $ \lt a , b\gt \cdot \lt c, d \gt =ac+bd$ We have: $u=\lt -2, 1 \gt $ and $v = \lt 3, 4 \gt $ and $w= \lt -5, 12 \gt $ Now, $v-w= \lt 3, 4 \gt - \lt -5, 12 \gt =\lt 3+5, 4, -12 \gt = \lt 8, -8 \gt $ Therefore, $u \cdot (v-w) = \lt -2, 1 \gt \cdot \lt 8, -8 \gt \\= (-2)(8) +(1)(-8) \\= -16-8 \\=-24$
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