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: 29



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: $det =3u \times v =[(-9)(2)-(3)(3)] i -j [(6)(2) - (3)(-3)]+k [(6)(3) -(-9) (-3)]=-27i-21j-9k$
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