Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 9 - Polar Coordinates; Vectors - Chapter Review - Review Exercises - Page 635: 43

Answer

$3i+9j+9k.$

Work Step by Step

We know that for a matrix \[ \left[\begin{array}{rrr} a & b & c \\ d &e & f \\ g &h & i \\ \end{array} \right] \] the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$ We know that if we have two vectors $v=ai+bj+ck$ and $w=di+ej+fk$, then $v\times w$ can be obtained by the determinant of: \[ \left[\begin{array}{rrr} i & j & k \\ a &b & c \\ d &e & f \\ \end{array} \right] \] Hence here $D=u\times w=i(1\cdot(-1)-(-2)\cdot2)-j(3\cdot(-1)-(-2)\cdot(-3))+k(3\cdot2-1\cdot(-3))=3i+9j+9k.$
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