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Un vector  tiene componentes . Hallar las coordenadas de  si se conoce el extremo .

The problem asks to find the coordinates of a vector \(\vec{A}\) given its components and the coordinates of one endpoint.

From the image:
- The components of the vector \(\vec{A}\) are \( \vec{A} = \langle -5, 2 \rangle \).
- The coordinates of the known endpoint are \( B = (12, 3) \).

Let's denote the unknown endpoint of the vector as \( A = (x, y) \).

The components of the vector \(\vec{A}\) are found by subtracting the coordinates of point \( B \) from \( A \):
\[
\vec{A} = \langle x - 12, y - 3 \rangle
\]
We are given that:
\[
\langle x - 12, y - 3 \rangle = \langle -5, 2 \rangle
\]

This gives us the following system of equations:
\[
x - 12 = -5
\]
\[
y - 3 = 2
\]

### Solving the system:
1. For the \( x \)-coordinate:
   \[
   x = -5 + 12 = 7
   \]

2. For the \( y \)-coordinate:
   \[
   y = 2 + 3 = 5
   \]

Thus, the coordinates of point \( A \) are \( (7, 5) \).

### Final Answer:
The coordinates of \( A \) are \( (7, 5) \).

---

Would you like to go over the details or have any further questions? Here are some additional questions you might consider:

1. How are vector components calculated between two points?
2. What are some methods to visualize vectors in 2D space?
3. Can you explain how the direction of a vector affects its components?
4. How do you determine the length of a vector given its components?
5. How would you solve the problem if the vector had 3D components?

**Tip:** When working with vectors, always remember that the direction and magnitude are key to understanding how they behave in space.

Learn how to find the coordinates of a vector endpoint given its components and one endpoint. This math problem involves vector components and coordinate geometry. Step-by-step solution provided.

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