Given two points - $A(x_o, y_o, z_o)$, and $B(x_1, y_1, z_1)$
The points of course being arbitrary. I have to find $\vec{AB}$, and the unit vector $\frac{\vec{AB}}{||\vec{AB}||}$.
My method was the following: \begin{align} \vec{AB}&=\vec{OB}-\vec{OA}=<x_1,y_1,z_1>-<x_o,y_o,z_o> \\ \vec{AB}&= <x_1-x_0,y_1-y_o,z_1-z_o> \end{align} From here I can calculate the norm of the vector as the distance between the two points as the following. The norm of the vector I got for the arbitrary points vector was the following: $$\vec{u}=\frac{\vec{AB}}{||\vec{AB}||}=\frac{<x_1-x_0,y_1-y_o,z_1-z_o>}{\sqrt{(x_1-x_0)^2+(y_1-y_o)^2+(z_1-z_o)^2}}$$
Is my process the correct one for finding the vector $\vec{AB}$, and its unit vector?