$\begingroup$If $||v|| = 5$ and $||w|| = 3$, what are the smallest and largest values of $||v - w||$? What are the smallest and largest values of $v \cdot w$?
How can I solve these two problems? For $||v - w||$ how can you have different values when it is clear that the magnitude of v and w are given?
$\endgroup$11 Answer
$\begingroup$Hints:
- Triangle inequality $\|v+w\| \leq \|v\| + \|w\|$
- Cauchy-Schwarz inequality $|v \cdot w| \leq \|v\|\|w\|$
