https://file.aiquickdraw.com/mathbot/file/1728341074907ntl9xtyo.jpg

Name each vector, then write the vector in component form.

Let's break down both vectors from the given image:

### Vector 5 (from \( T \) to \( S \)):
1. The coordinates of \( T \) are approximately \( (2, 6) \).
2. The coordinates of \( S \) are approximately \( (6, 3) \).

To write the vector in component form, we subtract the coordinates of the initial point \( T \) from the terminal point \( S \):

\[
\text{Vector } \mathbf{TS} = (x_2 - x_1, y_2 - y_1) = (6 - 2, 3 - 6) = (4, -3)
\]

So, the vector \( \mathbf{TS} \) in component form is \( \mathbf{TS} = \langle 4, -3 \rangle \).

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### Vector 6 (from \( E \) to \( F \)):
1. The coordinates of \( E \) are approximately \( (-4, 4) \).
2. The coordinates of \( F \) are approximately \( (2, -3) \).

To write the vector in component form, we subtract the coordinates of \( E \) from \( F \):

\[
\text{Vector } \mathbf{EF} = (x_2 - x_1, y_2 - y_1) = (2 - (-4), -3 - 4) = (2 + 4, -3 - 4) = (6, -7)
\]

So, the vector \( \mathbf{EF} \) in component form is \( \mathbf{EF} = \langle 6, -7 \rangle \).

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Would you like any further details or explanations? Here are 5 related questions that can expand on this:

1. How do you calculate the magnitude of a vector from its component form?
2. What is the direction of each vector, and how can it be found using the components?
3. Can you visualize the resultant vector if you add \( \mathbf{TS} \) and \( \mathbf{EF} \)?
4. How would the vectors change if the points were translated by a certain amount?
5. What does it mean for two vectors to be parallel or perpendicular?

**Tip:** When writing vectors in component form, remember the order matters. Always subtract the coordinates of the initial point from the terminal point.

Learn how to find the component form of vectors by subtracting coordinates of points. Examples include vectors between points T to S and E to F. Suitable for students in Grades 8-10.

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