Let $u$ and $v$ in $\mathbb R^n$. Evaluate $\|3u - 2v\|$ given that $\|u\| = 4, \|v\| = 5$, and $u\cdot v= 3$

Question

I kind of see the reason why I need dot product in here, but I don't know how to use the dot product to help me figure out this question.

Answer 1

$$ \|3u-2v\|^2 = (3u-2v)\cdot(3u-2v) = (9u\cdot u) -(12u\cdot v) + (4v\cdot v). $$