Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 9 - Section 9.5 - The Cross Product - 9.5 Exercises - Page 665: 17

Answer

$\lt 0,2,2 \gt$ or, $2j+2k$

Work Step by Step

The cross product is defined as: $u \times v=\begin{vmatrix}i&j&k\\m_1&m_2&m_3\\n_1&n_2&n_3\end{vmatrix}=\lt m_2n_3-m_3n_2, m_3n_1-m_1n_3, m_1n_2-m_2b_1 \gt$ Let us consider $u=\overrightarrow {PQ}$ and $v=\overrightarrow {PR}$ Then, the vector perpendicular to the plane passing throght the points P,Q,R can be written as $u \times v$. Now, $u \times v=\lt (1)(0)-(-1)(0),(-1)(-2)-(1)(0), (1)(0) -(1)(-2) \gt=\lt 0,2,2 \gt$ or, $2j+2k$
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