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: 36

Answer

$-25$

Work Step by Step

Suppose that the two vectors can be represented as: $v=v_1i+v_2j+v_3k$ and $w=w_1i+w_2j+w_3k$, then their cross product of such vectors can be obtained in the form of determinate as : $ v \times w=\begin{vmatrix} i & j & k \\ v_1 & v_2 & v_3 \\ w_1 & w_2 & w_3 \\ \end{vmatrix}=(v_2w_3-v_3w_2)i-(v_1w_3-v_3w_1)j+(v_1w_2-v_2w_1)k$ Here,we have the cross product of two given vectors as : $u \times v =\begin{vmatrix} i & j & k \\ 2 & -3 & 1 \\ -3 & 3 & 2 \\ \end{vmatrix}=[(-6-3] i -j [4+(-3)]+k [6-9]=-9i-7j-3k$ Now, the dot product is: $(u \times v) \cdot w=(-9i-7j-3k)\cdot(i +j +3k)=(-9)(1)+(-7)(1)+(-3)(3)=-25$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.