Question

In Problems 45–50, find the unit vector in the same direction as v.

$v=-3j$

Short answer

The unit vector in the same direction as $v=-3j$is $-j$

Step-by-step solution

Step 1. Given

The vector $v=-3j$

To find the unit vector.

Step 2. Unit vector in the direction of v 

For any nonzero vector v, the vector $u=\frac{v}{||v||}$is a unit vector that has the same direction as v.

Step 3. Find v

Now,

$$\begin{gathered} ||v||=||-3j|| \\ =\sqrt{{(-3)}^2} \\ =\sqrt{9} \\ =3 \end{gathered}$$

Step 4. Find the unit vector.

The unit vector is,

$$\begin{gathered} u=\frac{v}{||v||} \\ =\frac{-3j}{3} \\ =-j \end{gathered}$$