We are given two points A and B with coordinates A(3, 2) and B(5, 6). We need to find the column vector $\vec{AB}$.

1. Problem Description

We are given two points A and B with coordinates A(3, 2) and B(5, 6). We need to find the column vector $\vec{AB}$.

2. Solution Steps

To find the column vector $\vec{AB}$, we subtract the coordinates of point A from the coordinates of point B.

If $A = (x_1, y_1)$ and $B = (x_2, y_2)$, then the vector $\vec{AB}$ is given by

$\vec{AB} = \begin{pmatrix} x_2 - x_1 \\ y_2 - y_1 \end{pmatrix}$.

In our case, $A = (3, 2)$ and $B = (5, 6)$. Therefore,

$\vec{AB} = \begin{pmatrix} 5 - 3 \\ 6 - 2 \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \end{pmatrix}$.

3. Final Answer

The column vector $\vec{AB}$ is $\begin{pmatrix} 2 \\ 4 \end{pmatrix}$.