Vector Mag: When Does u+w > mag(u)+mag(w)?

[KatlynEdwards]

Homework Statement

If a vector "u" is added to a vector "w", under what circumstances will the value of mag(u+w) ever be greater than mag(u)+mag(w)?

Homework Equations

Magnitude = Sqrt( (Sum of x components)^2 + (sum of y components)^2 )

The Attempt at a Solution

I really, have no idea where to begin... I guess I could set up an equation and try to solve for the variables... Could someone point me in the right direction?

Thanks for all the help!

 

[D H]

Think of your two vectors as representing two sides of a triangle, and their sum as the third side of the triangle. What is the longest possible length that that third side in terms of the lengths of sides u and w?

Note: You either have to extend the concept of triangle here a bit to accommodate the cases where u and v are parallel or antiparallel, or you can cover those as special cases.