University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 11 - Section 11.4 - The Cross Product - Exercises - Page 623: 44



Work Step by Step

$\vec{AB}= 16\hat{i}-5\hat{j}$ $\vec{AC}= 4\hat{i}+ 4\hat{j}$. $\vec{AB}\times\vec{AC}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\16&-5&0\\4&4&0\end{vmatrix}$$=(64+20)\hat{k}= 84\hat{k}$. $|\vec{AB}\times\vec{AC}|=\sqrt {84^{2}}= 84$. Area of the triangle = $\frac{1}{2}|\vec{AB}\times\vec{AC}|=\frac{1}{2}\times84=42$
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