Vector question: If |u| = 10 and |v| = 5, then |u + v| ....

[Fullmetal_Hye]

 

[pka]

Do you know about the triangle inequality?
\(\displaystyle \L
\left\| {u + v} \right\| \le \left\| u \right\| + \left\| v \right\|\)

 

[Fullmetal_Hye]

OH :shock:

..................

 

[pka]

OH :shock:

OH YES! In fact we can show that:
\(\displaystyle \L
\left| {\left\| u \right\| - \left\| v \right\|} \right| \le \left\| {u + v} \right\| \le \left\| u \right\| + \left\| v \right\|\)