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How do you find out the projection of a vector u on a vector w

How do you find out the projection of a vector u on a vector w

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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How do you find out the projection of a vector \( \mathbf{u} \) on a vector \( \mathbf{w} \)? - ○ The answer is the vector \( \mathbf{w} \) multiplied by a constant \( k \). That constant \( k \) is nothing but the dot product \( \mathbf{u} \cdot \mathbf{w} \) divided by the square of the norm of \( \mathbf{w} \). - ○ You multiply \( \mathbf{u} \) by \( \mathbf{w} \) as the cross product and you divide by \( w^2 \). - ○ You find the angle between \( \mathbf{u} \) and \( (\ \mathbf{w} \) \) and make sure that angle is 90 degrees. - ○ You project \( \mathbf{u} \) on the space. - ○ It is like projecting a movie on your wall.
Transcribed Image Text:How do you find out the projection of a vector \( \mathbf{u} \) on a vector \( \mathbf{w} \)? - ○ The answer is the vector \( \mathbf{w} \) multiplied by a constant \( k \). That constant \( k \) is nothing but the dot product \( \mathbf{u} \cdot \mathbf{w} \) divided by the square of the norm of \( \mathbf{w} \). - ○ You multiply \( \mathbf{u} \) by \( \mathbf{w} \) as the cross product and you divide by \( w^2 \). - ○ You find the angle between \( \mathbf{u} \) and \( (\ \mathbf{w} \) \) and make sure that angle is 90 degrees. - ○ You project \( \mathbf{u} \) on the space. - ○ It is like projecting a movie on your wall.
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Projection of vector u on w is nothing but the dot product of u and w divided by magnitude of vector w.

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