Question

find the unit vector in the same direction as $v$

$v=-3j$

$v=-3j$

Short answer

The unit vector in the direction of the vector$v=-3j$is$u=-j$

Step-by-step solution

Step 1. Given data

The given vector is

$v=-3j$

Step 2. Finding the magnitude of the given vector

The magnitude of the vector$v=-3j$ is:

$$\begin{gathered} \left|v\right|=\sqrt{{(-3)}^2} \\ \Rightarrow \left|v\right|=3 \end{gathered}$$

Step 3. Finding the unit vector

Unit vector u in the direction of v is

$u=\frac{v}{\left|\left|v\right|\right|}$.

Substitute the values of vector and magnitude vector in the formula.

$$\begin{gathered} u=\frac{-3j}{\left|\left|3\right|\right|} \\ \Rightarrow u=\frac{-3j}{3} \\ \Rightarrow u=-j \end{gathered}$$