u   =   (3, 4)T 
| u | = 5

v   =   (3, -4)T 
| v | = 5

w   =   u + v = (6, 0)T 
| w | = 6

Another Example

That was too easy. Usually vector elements are not convenient integer values. Here are some more realistic vectors, represented by the column matrices:

q   =   (2.2, 3.6)T
r   =   (-4.8, -2.2)T
s   =   q + r

Of course, the pythagorean formula still applies:

| (x, y)T |   =   ( x2 + y2 )

But now you will have to get out a calculator (or click on the calculator in Windows).