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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. 44 (page 603)

find each quantity if $v = 3 i - 5 j$ and $w = - 2 i + 3 j$
$||v + w||$

Short Answer

Expert verified

The value of $||v + w||$ when $v = 3 i - 5 j$ and $w = - 2 i + 3 j$ is $\sqrt{5}$

Step by step solution

01

Step 1. Given data

$v = 3 i - 5 j$ and $w = - 2 i + 3 j$

02

Step 2. Find the exact valueSubstitute the values of v and w in the equation v+w

$v + w = 3 i - 5 j - 2 i + 3 j$

$v + w = i - 2 j$

03

Step 3. Find the magnitude

$||v + w|| = \sqrt{1^{2} + 2^{2}}$

$||v + w|| = \sqrt{1 + 4}$

$||v + w|| = \sqrt{5}$

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