# Become a Linear Algebra Expert

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Directed Line Segment

To find the vector that forms between two points, you subtract two points. For example, if we have point $p = (P_1,P_2,P_3)$ and $q = (Q_1,Q_2,Q_3)$, then the vector that is going to form that connects from P to Q is:

\begin{equation}

\begin{split}

\vec{PQ} &= q – p\\

\vec{PQ} &= \begin{bmatrix}Q_1-P_1\\Q_2-P_2\\Q_3-P_3\end{bmatrix}

\end{split}

\end{equation}

Same procedure extends to $\mathbb{R}^n$