To write the vector in component form, we will determine the coordinates of points $A$ and $B$, and then subtract the coordinates of $B$ from $A$.

From the graph:

• Point $A$ has coordinates $(4, 3)$.
• Point $B$ has coordinates $(-2, 1)$.

The component form of the vector $\vec{AB}$ is calculated as: $\vec{AB} = (x_2 - x_1, y_2 - y_1)$ where $(x_1, y_1)$ are the coordinates of $B$ and $(x_2, y_2)$ are the coordinates of $A$.

$\vec{AB} = (4 - (-2), 3 - 1) = (4 + 2, 2) = (6, 2)$

Final Answer:

The vector in component form is: $\vec{AB} = (6, 2)$

Would you like an explanation of how to calculate magnitude or direction?

Expanding Questions:

1. How do you calculate the magnitude of a vector?
2. How can you determine the direction (angle) of a vector?
3. What does the component form tell us about a vector's movement?
4. How do vectors differ from points on a graph?
5. Can you write the unit vector corresponding to $\vec{AB}$?

Tip: Always plot vectors from tail to head to ensure clarity when interpreting components.