: Here is an interesting result about differentiating a Dot-product of two vector valued functions: Let v(t) = < v,(t), v2(t), v3 (t) > and w(t) = < w,(t), w2(t), w3 (t) > be two vector valued functions. Define the function f(t) = v(t) · w(t) (dot product) Find f'(t), and then say something about why this is “interesting".

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...
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: Here is an interesting result about differentiating a Dot-product of two vector
valued functions:
Let v(t) = < v,(t), v2(t), v3 (t) > and w(t) = < w,(t), w2(t), w3 (t) > be
two vector valued functions. Define the function
f(t) = v(t) · w(t) (dot product)
Find f'(t), and then say something about why this is “interesting".
Transcribed Image Text:: Here is an interesting result about differentiating a Dot-product of two vector valued functions: Let v(t) = < v,(t), v2(t), v3 (t) > and w(t) = < w,(t), w2(t), w3 (t) > be two vector valued functions. Define the function f(t) = v(t) · w(t) (dot product) Find f'(t), and then say something about why this is “interesting".
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