Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Section 12.4 - The Cross Product - Exercises 12.4 - Page 719: 44



Work Step by Step

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