Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - 12.4 The Cross Product - 12.4 Exercises - Page 862: 38


The given points are coplanar.

Work Step by Step

The points are coplanar if $AB \cdot (AC \times AD)=0$ $AB= \lt 2,-4,4 \gt$, $AC= \lt 4,-1,-2 \gt$, $AD= \lt 2,3,-6 \gt$ $AC \times AD=\lt 4,-1,-2 \gt \times\lt 2,3,-6 = \lt 12,20,14 \gt$ $AB \cdot (AC \times AD)= \lt 2,-4,4 \gt \cdot \lt 12,20,14 \gt$ $=24-80+56$ $=0$ Hence, the given points are coplanar.
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