Scalar product to prove triangle inequality?

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Homework Help Overview

The discussion revolves around proving the triangle inequality |a+b| <= |a| + |b| using the scalar product inequality |a.b| <= |a||b|. Participants are exploring the relationship between vector addition and the properties of magnitudes in the context of vector mathematics.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants suggest starting with the Pythagorean identities and consider the range of trigonometric functions. There is also a mention of expanding the expression |a+b|^2 to facilitate the proof.

Discussion Status

The discussion is ongoing, with various approaches being proposed. Some participants are questioning the initial understanding of the problem, while others are providing different mathematical strategies to tackle the proof.

Contextual Notes

There appears to be some uncertainty regarding the initial setup and the application of trigonometric identities in the context of vector magnitudes.

8emnero8
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Homework Statement


From the inequality

|a.b| <= |a||b|

prove the triangle inequality:

|a+b| <= |a| + |b|

Homework Equations



a.b = |a|b| cos theta

The Attempt at a Solution



Making a triangle where side c = a+b. Don't know how to approach the question.

Thanks.
 
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I may not be understanding your question, but it seems like you should start with the Pythagorean Identities.
 
Also think about what values your trig function is between
 
You should start by knowing |a+b|^2=(a+b).(a+b). Now expand the right side.
 

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