https://file.aiquickdraw.com/mathbot/file/1729272828453mg3kq3w4.jpg

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!

Vector c⃗ has initial point (5,0) and terminal point (-4,3). Write the vector in component form.

Learn how to find the component form of vector c⃗ with an initial point of (5,0) and terminal point of (-4,3). This detailed solution includes applying the formula ⟨x₂ - x₁, y₂ - y₁⟩ to find the vector ⟨-9, 3⟩. Suitable for high school students.

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