Let à E R?. Let ỹ be a vector field and C be a curve. Show that V ds = . ỹ ds. ntegration of a vector function is defined to be the vector given by ntegrating each component. That is: felf, 9) ds is by definition equa n(l f de C ade)

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.1: Length And Dot Product In R^n
Problem 17E: Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of...
icon
Related questions
icon
Concept explainers
Question

Hi, Im stuck on how to prove this following problem relating to vector fields, thank you!

Let à E R?. Let V be a vector field and C be a curve. Show that
Ä.
V ds:
Ä · V ds.
Integration of a vector function is defined to be the vector given by
integrating each component. That is: Self,9) ds is by definition equal
to (Sef ds, ſe g ds).
Transcribed Image Text:Let à E R?. Let V be a vector field and C be a curve. Show that Ä. V ds: Ä · V ds. Integration of a vector function is defined to be the vector given by integrating each component. That is: Self,9) ds is by definition equal to (Sef ds, ſe g ds).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Integration
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning