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

[shane1]

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

 

[courtrigrad]

consider the direction, and it is basically the triangle inequality.

 

[radou]

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.