Given a vector begins at (-2, 1) and ends at (3, -4) then the components of the vector are

To find the components of the vector that begins at point \((-2, 1)\) and ends at point \((3, -4)\), we subtract the coordinates of the starting point from the coordinates of the ending point.

The formula for finding the components of the vector is:
\[
\text{Vector components} = (x_2 - x_1, y_2 - y_1)
\]
where \((x_1, y_1)\) is the starting point and \((x_2, y_2)\) is the ending point.

Substituting the given points:
\[
x_1 = -2, \quad y_1 = 1
\]
\[
x_2 = 3, \quad y_2 = -4
\]

Now, calculate the components:
\[
\text{Vector components} = (3 - (-2), -4 - 1)
\]
\[
\text{Vector components} = (3 + 2, -4 - 1)
\]
\[
\text{Vector components} = (5, -5)
\]

So, the components of the vector are \((5, -5)\).

Would you like details or have any questions?

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Here are 5 related questions:
1. How do you calculate the magnitude of this vector?
2. What is the direction of the vector in degrees or radians?
3. How would you represent this vector graphically?
4. How do the vector components relate to unit vectors?
5. How does changing the starting point affect the vector components?

**Tip:** Always remember to subtract the coordinates of the initial point from the terminal point when finding vector components.

Learn how to find the components of a vector that starts at (-2, 1) and ends at (3, -4). This problem involves subtracting coordinates and understanding vector components. Suitable for Grades 9-12 students.

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