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Answer:

u   =   (3, 4)T
|u| = 5

v   =   (3, -4)T
|v| = 5

w    =   u + v  = (6, 0)T
|w| = 6

And 6 < 5 + 5, demonstrating that | u + v | <= | u | + | v |

Another Example

That was too easy. Usually vector elements are not convenient integer values. Here are some vectors, represented by column matrices with decimal fractions in their elements:

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

Of course, the Pythagorean formula still applies, but you will need a calculator to use it.

| (x, y)T |   =   Sqrt( x2 + y2 )

QUESTION 7:

What are the lengths of the vectors?

| q | = 

| r | =

| s | =