1.4: Vectors from a direction and from an angle

The vector $\mathbf{v}$ has a magnitude of $3\sqrt{5}$ units and has the same direction as $\mathbf{i} - 2\mathbf{j}$. Find $\mathbf{v}$ giving your answer in the form $a\mathbf{i} + b\mathbf{j}$, where $a$ and $b$ are integers.

The velocity vector $\mathbf{w}$ makes an angle of $30\degree$ with the positive $x$-axis and is such that $|\mathbf{w}| = 2$. Find $\mathbf{w}$ giving your answer in the form $\sqrt{c}\,\mathbf{i} + d\mathbf{j}$, where $c$ and $d$ are integers.