Let the vector vv have an initial point at left parenthesis, minus, 4, comma, 0, right parenthesis(−4,0) and a terminal point at left parenthesis, 0, comma, minus, 6, right parenthesis(0,−6). Determine the components of vector v, .v.

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.

Let the vector v have an initial point at (-4, 0) and a terminal point at (0, -6). Determine the components of vector v.

Learn how to calculate the components of a vector with initial point (-4, 0) and terminal point (0, -6). This detailed solution uses vector geometry and coordinate geometry, applying the basic vector component theorem. Suitable for students in Grades 9-12.

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