To write the vector $\mathbf{v}$ in component form, subtract the coordinates of the initial point from the coordinates of the terminal point:

$\mathbf{v} = (\text{terminal point} - \text{initial point})$

Given:

• Initial point: $(0,0)$
• Terminal point: $(-3,-2)$

$\mathbf{v} = (-3 - 0, -2 - 0) = (-3, -2)$

Thus, the vector in component form is:

$\mathbf{v} = (-3, -2)$

Would you like to see more details about vectors or their properties?

---

Related Questions:

1. How do you calculate the magnitude of a vector?
2. What is the direction of the vector $\mathbf{v} = (-3, -2)$?
3. How do you find a unit vector in the same direction as $\mathbf{v}$?
4. Can you explain how to add or subtract vectors in component form?
5. How do you calculate the dot product of two vectors?

Tip:

Always remember that vector components are calculated by subtracting the corresponding coordinates of the initial point from those of the terminal point.