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.