Assertion: `vec(A)xxvec(B)` is perpendicualr to both `vec(A)-vec(B)` as well as `vec(A)+vec(B)`
Reason: `vec(A)+vec(B)` as well as `vec(A)-vec(B)` lie in the plane containing `vec(A)` and `vec(B)`, but `vec(A)xxvec(B)` lies perpendicular to the plane containing `vec(A)` and `vec(B)`.

Options

A. If both Assetion and Reason are correct but Reason is the correct explanation of Assertion.
B. If both Assetion and Reason are correct but Reason is not the correct explanation of Assertion.
C. If Asserion is true but Reason is false
D. If Asserion is false but Reason is true

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that the vector product \(\vec{A} \times \vec{B}\) is perpendicular to both \(\vec{A} - \vec{B}\) and \(\vec{A} + \vec{B}\).
- To verify this, we need to recall that the cross product of two vectors results in a vector that is perpendicular to the plane formed by the two original vectors.

2. **Understanding the Reason**:
- The reason explains that \(\vec{A} + \vec{B}\) and \(\vec{A} - \vec{B}\) lie in the same plane as \(\vec{A}\) and \(\vec{B}\).
- Since \(\vec{A} \times \vec{B}\) is perpendicular to the plane containing \(\vec{A}\) and \(\vec{B}\), it must also be perpendicular to any vector that lies in that plane, including \(\vec{A} + \vec{B}\) and \(\vec{A} - \vec{B}\).

3. **Mathematical Representation**:
- We can express the vectors as follows:
- \(\vec{C} = \vec{A} + \vec{B}\)
- \(\vec{D} = \vec{A} - \vec{B}\)
- We need to show that \((\vec{A} \times \vec{B}) \cdot \vec{C} = 0\) and \((\vec{A} \times \vec{B}) \cdot \vec{D} = 0\).
- Using the properties of the dot product:
- \((\vec{A} \times \vec{B}) \cdot \vec{C} = (\vec{A} \times \vec{B}) \cdot (\vec{A} + \vec{B}) = (\vec{A} \times \vec{B}) \cdot \vec{A} + (\vec{A} \times \vec{B}) \cdot \vec{B} = 0 + 0 = 0\)
- Similarly, \((\vec{A} \times \vec{B}) \cdot \vec{D} = (\vec{A} \times \vec{B}) \cdot (\vec{A} - \vec{B}) = (\vec{A} \times \vec{B}) \cdot \vec{A} - (\vec{A} \times \vec{B}) \cdot \vec{B} = 0 - 0 = 0\)

4. **Conclusion**:
- Since both the assertion and reason are true and the reason correctly explains the assertion, we conclude that both statements are valid.

### Final Answer:
Both the assertion and reason are true, and the reason is the correct explanation of the assertion.