Assertion - Vector addition of two vector is always greater then their vector subtraction.
Reason At `theta =90^(@)` , addition and subtraction of two vector are equal .

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 addition of two vectors is always greater than their vector subtraction. Mathematically, if we have two vectors \( \vec{A} \) and \( \vec{B} \), we can express this as:
\[ |\vec{A} + \vec{B}| > |\vec{A} - \vec{B}| \]
for all angles \( \theta \) between them.

2. **Understanding the Reason**:
The reason states that at \( \theta = 90^\circ \), the addition and subtraction of two vectors are equal. We can express this mathematically as:
\[ |\vec{A} + \vec{B}| = |\vec{A} - \vec{B}| \]
when \( \theta = 90^\circ \).

3. **Calculating Magnitudes**:
- For vector addition:
\[ |\vec{A} + \vec{B}| = \sqrt{A^2 + B^2 + 2AB \cos \theta} \]
- For vector subtraction:
\[ |\vec{A} - \vec{B}| = \sqrt{A^2 + B^2 - 2AB \cos \theta} \]

4. **Substituting \( \theta = 90^\circ \)**:
- At \( \theta = 90^\circ \), \( \cos 90^\circ = 0 \):
- For addition:
\[ |\vec{A} + \vec{B}| = \sqrt{A^2 + B^2} \]
- For subtraction:
\[ |\vec{A} - \vec{B}| = \sqrt{A^2 + B^2} \]

5. **Conclusion**:
- From the calculations, we see that:
\[ |\vec{A} + \vec{B}| = |\vec{A} - \vec{B}| \]
- This means that at \( \theta = 90^\circ \), the assertion that vector addition is always greater than vector subtraction is false, while the reason is true.

6. **Final Answer**:
- The assertion is false, and the reason is true. Therefore, the correct option is that the assertion is false and the reason is true.