Given the following vector, $\(\mathbf{v}\)$, obtain the unit vector that aligns with the direction of $\(\mathbf{v}\)$.

$\(\mathbf{v}\)=3\(\mathbf{i}\)+4\(\mathbf{k}\)$

Given the following vector, $\(\mathbf{v}\)$, obtain the unit vector that aligns with the direction of $\(\mathbf{v}\)$.

$\(\mathbf{v}\)=-5\(\mathbf{i}\)+2\(\mathbf{j}\)$

A vector's magnitude is $8$ and it forms a $120^{\(\omicron\)}$ angle with the positive $x$-axis. How can this vector be represented in terms of $\(\mathbf{i}\)$ and $\(\mathbf{j}\)$?