a)$|u|+|v|$
b)$|-6u|+8|v|$
c)$|5u+4v+w|$
d)$\frac{1}{|w|}w$
e)$|\frac{1}{|w|}w|$
For $|u|+|v|$ I have: $\sqrt{5^2+4^2+3^2}+ \sqrt{(-4)^2+(-1)^2+(-1)^2}$ to get $\sqrt{50}+\sqrt{18}$. I do not believe this is the right technique. So then I tried $5i-4i+4j-j+3k-k$ to get $i+3j+2k$ which means $1+3+2=6$ which is also wrong. Therefore since I do not know how to do the first question, I do not know how to do the rest.
These are all straight forward, and you were right at the beginning. The answer to $a)$ simplifies to $8\sqrt2$. $e)$ is clearly $1$.
For the others just set them up and knock them down. Here's $b): 6(5\sqrt2)+8(3\sqrt2)=54\sqrt2$.
$c): 5u=(25,20,12),4v=(-16,-4,-4)\implies5u+4v+w=(9,16,8)+(4,4,-5)=(13,20,3)$. So we get $|5u+4v+w|=\sqrt{13^2+20^2+3^2}=\sqrt{578}$.