To find the components of the vector v, we subtract the coordinates of the initial point from the coordinates of the terminal point.

The formula to find the components of a vector is:

$\mathbf{v} = (x_2 - x_1, y_2 - y_1)$

Where:

• $(x_1, y_1)$ is the initial point,
• $(x_2, y_2)$ is the terminal point.

Given:

• Initial point: $(-4, 0)$,
• Terminal point: $(0, -6)$.

Now, calculate the components:

$\mathbf{v} = (0 - (-4), -6 - 0)$

Simplifying:

$\mathbf{v} = (0 + 4, -6) = (4, -6)$

Thus, the components of vector v are $\mathbf{v} = (4, -6)$.

Would you like a detailed breakdown of vector operations or more help with vectors? Here are some questions to explore further:

1. How do you find the magnitude of a vector from its components?
2. What is the direction of a vector, and how can it be calculated?
3. How do you add or subtract vectors with components?
4. What is a unit vector, and how do you find one from a given vector?
5. How do you perform scalar multiplication on a vector?

Tip: When calculating vector components, always subtract the initial point from the terminal point to get the correct direction of the vector.