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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. 23 (page 627)

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

Short Answer

Expert verified

u 脳 v = -9i-7j-3k

Step by step solution

01

Step 1. Given information

u = 2i - 3j + k

v = -3i + 3j + 2k

w = i + j + 3k

02

Step 2. u ×v

For two vectors

v=a₁i+b₁j+c₁k

w=a₂i+b₂j+c₂k

cross product v脳 w is written as

$v 脳 w = |\begin{matrix} i & j & k \\ a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \end{matrix}| = i |\begin{matrix} b_{1} & c_{1} \\ b_{2} & c_{2} \end{matrix}| - j |\begin{matrix} a_{1} & c_{1} \\ a_{2} & c_{2} \end{matrix}| + k |\begin{matrix} a_{1} & b_{1} \\ a_{2} & b_{2} \end{matrix}|$

u = 2i - 3j + k

v = -3i + 3j + 2k

$u 脳 v = |\begin{matrix} i & j & k \\ 2 & - 3 & 1 \\ - 3 & 3 & 2 \end{matrix}| = i |\begin{matrix} - 3 & 1 \\ 3 & 2 \end{matrix}| - j |\begin{matrix} 2 & 1 \\ - 3 & 2 \end{matrix}| + k |\begin{matrix} 2 & - 3 \\ - 3 & 3 \end{matrix}| = - 9 i - 7 j - 3 k$

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