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: 32


$- 21i -33j +18k$

Work Step by Step

Let us consider two vectors $v=xi+yj+zk$ and $w=pi+qj+rk$. Then the cross product of the two vectors $v$ and $w$ can be computed in the form of the determinant as: $ v \times w=\begin{vmatrix} i & j & k \\ x & y & z \\ p & q & r \\ \end{vmatrix}$ We have: $det =-3v \times w =[(-9)(3)-(-6)(1)] i -j [(9)(3) - (-6)(1)]+k [(9)(1) -(-3) (-6)]=- 21i -33j +18k$
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