Express the vector as a sum of two vectors Express the vector $\vec{u}$ below as a sum of two vectors $\vec{u}_1$ and $\vec{u}_2$, where $\vec{u}_1$ is parallel to the vector $\vec{v}$ given below, and $\vec{u}_2$ is perpendicular to $\vec{v}$. Make sure that the first vector in your sum is $\vec{u}_1$ and the second is $\vec{u}_2$.
$\vec{v} = [-3,-1,1]$
$\vec{u} = [-2,-10,6] = [-,-,-]+[-,-,-] = \vec{u}_1 + \vec{u}_2$
NOTE: Everything is vertical vectors but I dont know how to write it like that. I need to fill in the 2 vectors where it is has dashes. Can someone show me how to do this? I don't know how to solve these questions. 

Write
$$
   u
 = proj_v u + (u-proj_v u)
:= u_1 + u_2.
$$
So in your case you would get
$$
  u_1
= \left(\frac{|u|\cdot |v|}{|v| \cdot |v|}\right)v
= \frac{22}{11}(-3,-1,1)
= (-6,-2,2)
$$
and 
$$
  u_2
= (-2,-10,6) - (-6,-2,2)
= (4,-8,4).
$$
