Answer
$-\frac{1}{\sqrt{5}}\mathbf{i}-+\frac{2}{\sqrt{5}}\mathbf{j}$
Work Step by Step
Unit vector:
For any vector $\mathbf{v}$, $\frac{\mathbf{v}}{\left\| \mathbf{v} \right\|}$ is the unit vector in the same direction as the vector $\mathbf{v}$.
Magnitude of vector is given by:
The magnitude of $\mathbf{v}=a\mathbf{i}+b\mathbf{j}$ is given by $\left\| \mathbf{v} \right\|=\sqrt{{{a}^{2}}+{{b}^{2}}}$.
Scalar multiplication of a vector is given by:
For any vector $\mathbf{v}=a\mathbf{i}+b\mathbf{j}$ and $k$ is a real number, $k\mathbf{v}=\left( ka \right)\mathbf{i}+\left( kb \right)\mathbf{j}$.
Here, $\mathbf{v}=-\mathbf{i}+2\mathbf{j}$.
So,
$\begin{align}
& \left\| \mathbf{v} \right\|=\sqrt{{{\left( -1 \right)}^{2}}+{{2}^{2}}} \\
& =\sqrt{1+4} \\
& =\sqrt{5}
\end{align}$
The unit vector in the direction as the vector $\mathbf{v}$ is calculated as below:
$\begin{align}
& \frac{\mathbf{v}}{\left\| \mathbf{v} \right\|}=\frac{-\mathbf{i}+2\mathbf{j}}{\sqrt{5}} \\
& =-\frac{1}{\sqrt{5}}\mathbf{i}-+\frac{2}{\sqrt{5}}\mathbf{j}
\end{align}$
Hence, the unit vector in the direction as the vector $\mathbf{v}$ is $-\frac{1}{\sqrt{5}}\mathbf{i}-+\frac{2}{\sqrt{5}}\mathbf{j}$.
