A unit cell is defined by 3 base vectors
Any coordinate is within the unit cell (or outside of it) is defined as a linear combination of these vectors: [1 2 3]. If values aren't integers, then we multiply them to get integers.
$$ p = \begin{bmatrix}u_1 & u_2 & u_3\end{bmatrix} \begin{bmatrix}\underline{a_1} & \underline{a_2} & \underline{a_3}\end{bmatrix} = \begin{bmatrix}u_1 & u_2 & u_3\end{bmatrix} \begin{bmatrix}