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?In Exercises 1-8, find (a) \(\mathbf{u} \cdot \mathbf{v}\), (b) \(\mathbf{u} \cdot \mathbf{u}\), (c) \(\|\mathbf{u}\|^{2}

Calculus: Early Transcendental Functions | 6th Edition | ISBN: 9781285774770 | Authors: Ron Larson ISBN: 9781285774770 141

Solution for problem 4 Chapter 11.3

Calculus: Early Transcendental Functions | 6th Edition

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Calculus: Early Transcendental Functions | 6th Edition | ISBN: 9781285774770 | Authors: Ron Larson

Calculus: Early Transcendental Functions | 6th Edition

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Problem 4

In Exercises 1-8, find

(a) \(\mathbf{u} \cdot \mathbf{v}\),

(b) \(\mathbf{u} \cdot \mathbf{u}\),

(c) \(\|\mathbf{u}\|^{2}\),

(d) \((\mathbf{u} \cdot \mathbf{v}) \mathbf{v}\), and

(e) \(\mathbf{u} \cdot(\mathbf{2 v})\).

\(\mathbf{u}=\langle-4,8\rangle, \mathbf{v}=\langle 7,5\rangle\)

Text Transcription:

u dot v

u dot u

||u||^2

(u dot v) v

u dot(2 v)

u=langle-4,8 rangle, v=langle 7,5 rangle

Step-by-Step Solution:

Step 1 of 5) To evaluate the integrals in Equations (5), we picture the plate in the coordinate plane and sketch a strip of mass parallel to one of the coordinate axes. We then express the strip’s mass dm and the coordinates (x , y ) of the strip’s center of mass in terms of x or y. Finally, we integrate y dm, x dm, and dm between limits of integration determined by the plate’s location in the plane.

Step 2 of 2

Chapter 11.3, Problem 4 is Solved
Textbook: Calculus: Early Transcendental Functions
Edition: 6
Author: Ron Larson
ISBN: 9781285774770

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?In Exercises 1-8, find (a) \(\mathbf{u} \cdot \mathbf{v}\), (b) \(\mathbf{u} \cdot \mathbf{u}\), (c) \(\|\mathbf{u}\|^{2}