To solve this problem, you need to find vector $\mathbf{a}$, represented by the directed line segment from point $A$ to point $B$. Typically, the coordinates for $A$ and $B$ would be provided, but since they aren't given, let's just discuss the general approach.

Steps:

1. Understand the Vector Representation:

   • A vector $\mathbf{a}$ from point $A(x_1, y_1)$ to point $B(x_2, y_2)$ can be represented as: $\mathbf{a} = \langle x_2 - x_1, y_2 - y_1 \rangle$

2. Draw $\overrightarrow{AB}$:

   • Plot the points $A$ and $B$ on a coordinate plane.
   • Draw a directed line segment (arrow) from $A$ to $B$.

3. Equivalent Representation from the Origin:

   • The vector $\mathbf{a}$ can also be represented starting from the origin $(0,0)$ to the point $(x_2 - x_1, y_2 - y_1)$.
   • Plot the point $(x_2 - x_1, y_2 - y_1)$ from the origin and draw a directed line segment (arrow).

Example:

If $A = (3, 2)$ and $B = (6, 5)$:

• The vector $\mathbf{a} = \langle 6 - 3, 5 - 2 \rangle = \langle 3, 3 \rangle$.

• Draw $\overrightarrow{AB}$ from (3, 2) to (6, 5).

• Draw the vector from origin to (3, 3).

This visualization shows the same vector starting from the origin, maintaining the direction and magnitude.