Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

The Component of $u$ along $v$
Find the component of $u$ along $v$ .
$u = ⟨ - 3, 5 ⟩, v = ⟨ 1 / \sqrt{2}, 1 / \sqrt{2} ⟩$

The component is $\sqrt{2}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

Vectors are given as-

$u = ⟨ - 3, 5 ⟩, v = ⟨ 1 / \sqrt{2}, 1 / \sqrt{2} ⟩$

Step 2. Concept used

The dot product of two vectors $u$ and $v$ can be defined as-

$u \cdot v = a_{1} b_{1} + a_{2} b_{2}$

Where $u = (a_{1}, a_{2}) & v = (b_{1}, b_{2})$

If $u$ and $v$ are two vectors then the component of $u$ along $v$ can be defined as $com p_{v} u = \frac{u \cdot v}{| v |}$

Use the formula of components of $u$ along $v$ and the dot product of vectors.

Step 3. Calculation

Component of $u$ along $v$ ,

$\begin{array}{l} {comp}_{v} u = \frac{u \cdot v}{| v |} \\ = \frac{- 3 \{\frac{1}{\sqrt{2}}\} + 5 \{\frac{1}{\sqrt{2}}\}}{\sqrt{{\{\frac{1}{\sqrt{2}}\}}^{2} + {\{\frac{1}{\sqrt{2}}\}}^{2}}} \\ = \frac{\sqrt{2}}{1} \\ = \sqrt{2} \end{array}$

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Precalculus Mathematics for Calculus

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Short Answer

The Component of $u$ along $v$
Find the component of $u$ along $v$ .
$u = ⟨ - 3, 5 ⟩, v = ⟨ 1 / \sqrt{2}, 1 / \sqrt{2} ⟩$

Step by Step Solution

Step 1. Given information

Step 2. Concept used

Step 3. Calculation

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Precalculus Mathematics for Calculus

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Short Answer

The Component of u along vFind the component of u along v.u=⟨-3,5⟩,v=⟨1/2,1/2⟩

Step by Step Solution

Step 1. Given information

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The Component of $u$ along $v$
Find the component of $u$ along $v$ .
$u = ⟨ - 3, 5 ⟩, v = ⟨ 1 / \sqrt{2}, 1 / \sqrt{2} ⟩$