DO THIS: Write a function that projects vector $v$ onto vector $u.$ Do not use the numpy library.

Make sure this function will work for any size of $v$ and $u.$Now, calculate a vector that is orthogonal to proj$\_($u$)$v$.[]$:Let's test your functions. Below there are two example vectors. Find the projection of v onto u and a vector othogonal to u$.$ Note that the order of variables in your function proj$(.,)$ matters! Make sure you get the correct answers.$[]$:

$u=[1,2,0,3]$

$v=[4,0,5,8]$

print$(proj(...))$

print$(orth(...))$

Now let's simplify these calculations using different libraries:

import numpy as np

$u=np*array([dots])$