How do you find the coordinate of a vector with the unit vector?

[BlueRope]

If you already have one of the two coordinates?

 

[Fredrik]

If $x=x_1e_1+x_2e_2$ and you know the value of $x_1$, you can get the value of $x_2$ from $x_2e_2=x-x_1e_1$.

Another option (if you understand inner products) is to just compute $\langle e_2,x\rangle$.