https://r2.erweima.ai/mathbot/image/1726286339692t31d3y2d.jpg

The image contains two sets of vectors and corresponding operations:

### Operations:
- \( a) \ 3a \)
- \( b) \ a + b \)
- \( c) \ a - b \)
- \( d) \ |a + b| \) (the magnitude of \( a + b \))
- \( e) \ |a - b| \) (the magnitude of \( a - b \))

### Vector sets:
1. \( \mathbf{a} = 2\mathbf{i} + 4\mathbf{j}, \ \mathbf{b} = -\mathbf{i} + 4\mathbf{j} \)
2. \( \mathbf{a} = \langle 1, 1 \rangle, \ \mathbf{b} = \langle 2, 3 \rangle \)

Would you like to calculate the operations for a specific set of vectors, or for both sets? Let me know which part you'd like to work on first.

### Follow-up questions:
1. Would you like to compute the result of \( 3a \) for both vector sets?
2. Should I calculate \( a + b \) for one or both sets of vectors?
3. Do you want to explore the vector magnitudes, such as \( |a + b| \)?
4. Should I explain the geometric meaning of the operations between these vectors?
5. Are you interested in a detailed explanation of vector addition and subtraction?

**Tip:** The magnitude of a vector \( \mathbf{v} = \langle v_1, v_2 \rangle \) is calculated using \( |\mathbf{v}| = \sqrt{v_1^2 + v_2^2} \).

Solve vector operations involving two sets of vectors, including the magnitude of vector sums and differences.

Explore the solution of vector operations involving vector addition, subtraction, and magnitude calculations. This problem includes detailed explanations and is suitable for high school students in Grades 10-12.

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