To find a unit vector in the direction of a vector given we just need to divide it by its magnitude, that is:
[tex]\mathbf{\hat{u}}=\frac{\mathbf{u}}{\lvert{\mathbf{u}}\rvert}[/tex]
The magnitude of a vector is given by:
[tex]\lvert{\mathbf{u}}\rvert=\sqrt{u_x^2+u_y^2}[/tex]
In this case we have:
[tex]\lvert{\mathbf{u}}\rvert=\sqrt{3^2+(-4)^2}=\sqrt{25}=5[/tex]
Hence the magnitude of the vector given is 5. Now that we know the magnitude of the vector we need to divide it by this. Therefore, to find a unit vector we multiply u by 1/5
