Question

In Problems 47–52, find the unit vector in the same direction as$v$:$v=2i-j$

Short answer

The unit vector in the same direction as $v$ is$\frac{2}{\sqrt{5}}i-\frac{1}{\sqrt{5}}j$

Step-by-step solution

Step 1. Magnitude of the Vector

The given vector is $v=2i-j$

The magnitude of the given vector is$$\begin{gathered} \sqrt{2^2+1^2}=\sqrt{4+1} \\ =\sqrt{5} \end{gathered}$$

Step 2. Unit Vector in the direction of v

Now, we multiply the scaler $\frac{1}{\left|v\right|}=\frac{1}{\sqrt{5}}$

A unit vector in the same direction as $v$is$\frac{v}{\Vert v\Vert }=\frac{2i-j}{\sqrt{5}}=\frac{2}{\sqrt{5}}i-\frac{1}{\sqrt{5}}j$