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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 26 (page 627)

Use the given vectors u, v, and w to find each expression.
$u = 2 i - 3 j + k, v = - 3 i + 3 j + 2 k, w = i + j + 3 k$
$w 脳 v$

Short Answer

Expert verified

The required cross product is $- 7 i - 11 j + 6 k$ .

Step by step solution

01

Step 1. Given Information

We are given three vectors $u, v, w$ and we need to find the cross product of $w 脳 v$ .

02

Step 2. Finding cross product

$v = - 3 i + 3 j + 2 k w = i + j + 3 k$

The required cross product is

$w 脳 v = |\begin{matrix} i & j & k \\ 1 & 1 & 3 \\ - 3 & 3 & 2 \end{matrix}| = i |\begin{matrix} 1 & 3 \\ 3 & 2 \end{matrix}| - j |\begin{matrix} 1 & 3 \\ - 3 & 2 \end{matrix}| + k |\begin{matrix} 1 & 1 \\ - 3 & 3 \end{matrix}| = i (1.2 - 3.3) - j (1.2 - (- 3) . 3) + k (1.3 - (- 3) . 1) = - 7 i - 11 j + 6 k$

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