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To write the vector \(\vec{v}\) in component form, you subtract the coordinates of the initial point from the coordinates of the terminal point.

The initial point is \( (1, -3) \) and the terminal point is \( (7, -9) \).

The formula for finding the vector in component form is:
\[
\vec{v} = (x_2 - x_1, y_2 - y_1)
\]
Where:
- \( (x_1, y_1) \) is the initial point
- \( (x_2, y_2) \) is the terminal point

So,
\[
\vec{v} = (7 - 1, -9 - (-3)) = (6, -6)
\]

Thus, the vector in component form is \( \vec{v} = \langle 6, -6 \rangle \).

Would you like further details or clarifications?

Here are 5 related questions:
1. How do you calculate the magnitude of a vector given in component form?
2. What is the geometric interpretation of a vector in component form?
3. How do you add two vectors in component form?
4. How do you find the direction angle of a vector from its components?
5. How would you normalize a vector in component form?

**Tip:** Always remember that subtracting the coordinates of the initial point from the terminal point gives you the displacement represented by the vector.

Vector →v has initial point (1, -3) and terminal point (7, -9). Write the vector in component form.

Learn how to find the vector in component form given the initial point (1, -3) and terminal point (7, -9). This problem covers key vector concepts, including the formula for vector components and how to apply it.

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