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: 61

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, $u \cdot v= \lt -2, 1 \gt \cdot \lt 3, 4 \gt =(-2)(3)+(1) (4)=-6+4=-2$ and $u \cdot w= \lt -2, 1 \gt \cdot \lt -5, 12 \gt =(-2)(-5)+(1) (12)=10+12=22$ $u \cdot v -u \cdot w = -2-22=-24$
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