https://r2.erweima.ai/mathbot/image/17268645149994xsyqfc4.jpg

Here are the results of the vector operations along with the graph:

1. \( 2\mathbf{u} = (-4, 10) \)
2. \( \frac{1}{2}\mathbf{u} = (-1, 2.5) \)
3. \( -2\mathbf{u} = (4, -10) \)
4. \( \mathbf{u} + \mathbf{v} = (1, 9) \)
5. \( \mathbf{u} - \mathbf{v} = (-5, 1) \)
6. \( \mathbf{u} + 2\mathbf{v} = (4, 13) \)

The plot shows each vector operation with a different color for clarity.

Would you like further details or clarifications? Here are some related questions to consider:

1. What do vector operations represent geometrically?
2. How do scalar multiplications affect vector direction and magnitude?
3. Can you explain why adding vectors changes their direction?
4. How do you find the magnitude of a vector?
5. What is the physical interpretation of subtracting two vectors?

**Tip:** When graphing vectors, their tail starts at the origin unless they represent position vectors starting from another point.

Dado los vectores u = (-2, 5) y v = (3, 4), obtenga lo indicado en cada inciso y grafique.

Explore vector operations with given vectors u = (-2, 5) and v = (3, 4). Learn how to perform scalar multiplication, vector addition, and subtraction step by step, with graphing examples. Ideal for high school students studying vectors.

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