Question

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

Short answer

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

Step-by-step solution

Step 1. Magnitude of the Vector

The given vector$\mathbf{v}=\mathbf{i}-j$

Th magnitude of the given vector is $\sqrt{1+1}=\sqrt{2}$

Step 2. Unit Vector in the direction of v

Now, we multiply the scaler $\frac{1}{\left|v\right|}=\frac{1}{\sqrt{2}}$. A unit vector in the same direction as $v$is:

$\frac{\mathbf{v}}{\Vert \mathbf{v}\Vert }=\frac{\mathbf{i}-\mathbf{j}}{\sqrt{2}}=\frac{1}{\sqrt{2}}\mathbf{i}-\frac{1}{\sqrt{2}}\mathbf{j}$