Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 12 - Review - Exercises - Page 842: 7


(a) 2 (b) -2 (c) -2 (d) 0

Work Step by Step

(a) Given: $u \cdot (v \times w)=2$ $(u \times v) \cdot w=2$ (b) Given: $u \cdot (v \times w)=2$ $u \cdot (w \times v)=u \cdot -(v \times w)$ $-(u \cdot (v \times w))=-2$ Thus, $u \cdot (w \times v)=-2$ (c) Given: $u \cdot (v \times w)=2$ $v \cdot (u \times w) = v \cdot -( w \times u)$ $=-(v \cdot (w \times u)$ $=-((v \times w) \cdot u)$ $=-u \cdot (v \times w)$ Thus, $v \cdot (u \times w) = -2$ (d) Given: $u \cdot (v \times w)=2$ Since $(u \times v) \perp v$; the dot product of the two vectors is $0$. Thus, $(u \times v) \cdot v=0$
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