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 - Practice Exercises - Page 734: 24



Work Step by Step

The cross product of parallel vectors is the zero vector. ${\bf (2i+4j-5k)}\times{\bf (-4i-8j+ak)}=\left|\begin{array}{rrr} {\bf i} & {\bf j} & {\bf k}\\ 2 & 4 & -5\\ -4 & -8 & a \end{array}\right|$ $=(4a-40){\bf i}-(2a-20){\bf j}+(16-16){\bf k}$ For this to be the zero vector, it must be that $\left\{\begin{array}{l} 4a-40=0\\ 2a-20=0 \end{array}\right.$ that is, $a=10.$
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