Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 8 - Polar Coordinates; Vectors - Section 8.7 The Cross Product - 8.7 Assess Your Understanding - Page 652: 46


$\sqrt {213}$

Work Step by Step

1. Find the vectors $\vec {P_1P_2}=< 2, 3, 1>$ $\vec {P_1P_3}=<-2,4,1>$ 2. Find the cross product $\vec {P_1P_2}\times\vec {P_1P_3} = <(3(1)-1(4)),(1(-2)-2(1)),(2(4)-3(-2))>=<-1,-4,14>$ 3. We have the area $A=||\vec {P_1P_2}\times\vec {P_1P_3} || =\sqrt {1^2+4^2+14^2}=\sqrt {213}$
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