Question

Prove this property of vectors:

Answer 1

\[||a||+||b||=||a+b||\]

Answer 2

By definition, if \[ ||\cdot|| \] is a norm in a vector space, then for all vectors a,b we have
\[ ||a+b|| \le ||a||+||b|| \]
Equality must not always hold!

Answer 3

This is called the triangle inequality.

Answer 4

ah. thanks