Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 9 - Polar Coordinates; Vectors - Chapter Review - Review Exercises - Page 635: 41



Work Step by Step

Perform the fubtraction first: \begin{align*} v-w&=(3i+j-2k)-(-3i+2j-k)\\ &=3i+j-2k+3i-2j+k\\ &=i(3+3)+j(1-2)+k(-2+1)\\ &=6i-j-k \end{align*} Recall that if $v=ai+bj+ck$, then the magnitude $||v||$ given by the formula: $||v||=\sqrt{a^2+b^2+c^2}$ Hence, \begin{align*} ||v-w||&=\sqrt{6^2+(-1)^2+(-1)^2}\\ &=\sqrt{36+1+1}\\ &=\sqrt{38} \end{align*}
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