Given the vectors <3, 4, 5> and B<-3, 5, -6> find A+B, A-B, and B-A

Let's calculate the vector operations one by one for vectors \( \mathbf{A} = \langle 3, 4, 5 \rangle \) and \( \mathbf{B} = \langle -3, 5, -6 \rangle \).

### 1. \( \mathbf{A} + \mathbf{B} \)
To add two vectors, add their corresponding components:

\[
\mathbf{A} + \mathbf{B} = \langle 3 + (-3), 4 + 5, 5 + (-6) \rangle
\]

\[
\mathbf{A} + \mathbf{B} = \langle 0, 9, -1 \rangle
\]

### 2. \( \mathbf{A} - \mathbf{B} \)
To subtract vector \( \mathbf{B} \) from vector \( \mathbf{A} \), subtract their corresponding components:

\[
\mathbf{A} - \mathbf{B} = \langle 3 - (-3), 4 - 5, 5 - (-6) \rangle
\]

\[
\mathbf{A} - \mathbf{B} = \langle 6, -1, 11 \rangle
\]

### 3. \( \mathbf{B} - \mathbf{A} \)
To subtract vector \( \mathbf{A} \) from vector \( \mathbf{B} \), subtract their corresponding components:

\[
\mathbf{B} - \mathbf{A} = \langle -3 - 3, 5 - 4, -6 - 5 \rangle
\]

\[
\mathbf{B} - \mathbf{A} = \langle -6, 1, -11 \rangle
\]

### Summary of results:
- \( \mathbf{A} + \mathbf{B} = \langle 0, 9, -1 \rangle \)
- \( \mathbf{A} - \mathbf{B} = \langle 6, -1, 11 \rangle \)
- \( \mathbf{B} - \mathbf{A} = \langle -6, 1, -11 \rangle \)

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:
1. What is the magnitude of vector \( \mathbf{A} \)?
2. How do you calculate the dot product of two vectors?
3. What is the result of the cross product \( \mathbf{A} \times \mathbf{B} \)?
4. How can you find the angle between vectors \( \mathbf{A} \) and \( \mathbf{B} \)?
5. What is the projection of vector \( \mathbf{A} \) onto vector \( \mathbf{B} \)?

**Tip:** When performing vector operations, always ensure you are matching the correct components to avoid sign errors in your calculations.

Explore vector addition and subtraction with an example problem. Learn how to calculate the sum and difference of vectors A and B, including step-by-step calculations and results. Suitable for high school students studying vectors and vector operations.

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