Answer
The required vector is $ \frac{12}{5}i+ \frac{9}{5}j $.
Work Step by Step
Since the vector is in the direction of $ v $ then it will be in the form $ av= 4ai+3aj $. Now, since the length is $3$, then we have
$$\sqrt{16a^2+9a^2}=\sqrt{25a^2}=3\Longrightarrow 5a=3\Longrightarrow a= \frac{3}{5}.$$
The required vector is $ \frac{12}{5}i+ \frac{9}{5}j $.
