## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson

# Chapter 8 - Polar Coordinates; Vectors - Section 8.7 The Cross Product - 8.7 Assess Your Understanding - Page 652: 38

#### 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 : $u \times v =\begin{vmatrix} i & j & k \\ -3 & 3 & 2 \\ 2 & -3 & 1 \\ \end{vmatrix}=[(-3)(3)-(2)(1)] i -j [(2)(3) - (1)(1)]+k [(2)(1) -(-3) (1)]=9i +7j +3k$ Now, the dot product is: $(u \times v) \cdot w=(9i+7j+3k) \cdot (i+j+3k)=(9)(1)+(7)(1) +(3)(3)=25$

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