To write the vector c in component form, we need to subtract the coordinates of the initial point from the terminal point.

The formula for the component form of a vector is:

$\vec{c} = \langle x_2 - x_1, y_2 - y_1 \rangle$

Where:

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

For the vector in your question:

• Initial point $(x_1, y_1) = (5, 0)$
• Terminal point $(x_2, y_2) = (-4, 3)$

Now, calculate the differences:

$\vec{c} = \langle -4 - 5, 3 - 0 \rangle = \langle -9, 3 \rangle$

So, the vector c in component form is:

$\langle -9, 3 \rangle$

Let me know if you'd like more details or have any questions!

Here are 5 related questions to expand on this:

1. How do you find the magnitude of vector $\vec{c}$?
2. What is the direction of the vector $\vec{c}$?
3. How do you express a vector as a unit vector?
4. What are some applications of vectors in physics?
5. How do you perform vector addition using component form?

Tip: Always subtract the initial point from the terminal point when finding the component form of a vector!