How can I use the dot product formula to find the angle between two vectors?

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Homework Help Overview

The discussion revolves around proving inequalities involving the norms of vectors V and U, specifically ||V - U|| and the absolute difference of their magnitudes. The context includes the application of the dot product formula to explore relationships between these vectors.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to manipulate the inequality involving the norms of the vectors and are questioning the correctness of their approaches. There is a focus on using the dot product and exploring the implications of the inequalities.

Discussion Status

Some participants have provided hints regarding the direction of the inequalities, while others are seeking further clarification and additional hints. The discussion reflects an ongoing exploration of the mathematical relationships without reaching a consensus.

Contextual Notes

There appears to be confusion regarding the direction of the inequalities, which is being actively discussed. Participants are also considering the implications of the triangle inequality in their reasoning.

leitz
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Homework Statement


Prove : ||V - U|| => | ||V||-||U|| |
V and U are vectors

Homework Equations


Maybe the dot product formula: ||A||*||B||cosθ

The Attempt at a Solution


==> ||V - U||2 >= (||V||-||U||)2
==> (V-U) . (V-U) >= ||V||2 +||U||2 - 2||U||*||V||
==> V.V + U.U -2U.V >= V.V + U.U - 2||U||*||V||
==> -2U . V >= -2 ||U||*||V||

I don't know how to go on from here. I always get a nonsensical answer if I try to simplify this. Am I using the right approach?
 
Last edited:
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leitz said:

Homework Statement


Prove : ||V - U|| <= | ||V||-||U|| |
V and U are vectors

Homework Equations


Maybe the dot product formula: ||A||*||B||cosθ

You have the inequality backwards above.

Hint: ||u|| = ||(u - v) + v|| ≤ ...
 
Can you give me another hint please?
 
LCKurtz said:
You have the inequality backwards above.

Hint: ||u|| = ||(u - v) + v|| ≤ ...

leitz said:
Can you give me another hint please?

What did you try with my hint? What might go after the ≤ ?
 

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