What is the difference between $|a|$ and $|| a ||$

Question

So I am doing maths involving cross-product and dot-product and I came across the above two notation as in $||u\times v|| = ||u|| ||v|| \sin a$ and $u\cdot v = |u| |v| \cos a$. What is the difference between $||u||$ and $|u|$?

Answer 1

These are different notations for the same thing: the magnitude of a vector.