Maximizing and Minimizing Norm of Vector v - w: A Geometric Explanation

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SUMMARY

The discussion centers on determining the maximum and minimum values of the norm of the vector difference ||v - w||, given ||v|| = 2 and ||w|| = 3. The largest value is achieved by adding the magnitudes, resulting in ||v - w|| = 5, while the smallest value is obtained by subtracting the magnitudes, yielding ||v - w|| = 1. This conclusion is supported by the triangle inequality theorem, which emphasizes the importance of vector direction in calculating the resultant magnitude.

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shane1
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I don't know if I'm just having a slow day or what is going on but I am being stumped by this:

If ||v|| = 2 and ||w|| = 3 what are the largest and smallest values possible for ||v - w||. Give a geometric explanation.

Would it be as simple as just adding the two values for the largest, and subtracting for the smallest?

Any help would be apreciated.

-Shane
 
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consider the direction, and it is basically the triangle inequality.
 
shane1 said:
I don't know if I'm just having a slow day or what is going on but I am being stumped by this:

If ||v|| = 2 and ||w|| = 3 what are the largest and smallest values possible for ||v - w||. Give a geometric explanation.

Would it be as simple as just adding the two values for the largest, and subtracting for the smallest?

Any help would be apreciated.

-Shane

Think about the direction of the two vectors.
 

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