Assertion (A+B).(A-B) is always positve.
Reason this is positive If `|A|gt|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 1: Understanding the Assertion
The assertion states that \((A + B) \cdot (A - B)\) is always positive. We need to evaluate this expression.

### Step 2: Expanding the Dot Product
Using the distributive property of the dot product, we can expand the expression:
\[ (A + B) \cdot (A - B) = A \cdot A - A \cdot B + B \cdot A - B \cdot B \]
Since the dot product is commutative (\(A \cdot B = B \cdot A\)), we can simplify this to:
\[ A \cdot A - B \cdot B = |A|^2 - |B|^2 \]

### Step 3: Analyzing the Result
The expression \( |A|^2 - |B|^2 \) can be positive, negative, or zero depending on the magnitudes of \(A\) and \(B\):
- If \(|A| > |B|\), then \( |A|^2 - |B|^2 > 0\).
- If \(|A| < |B|\), then \( |A|^2 - |B|^2 < 0\).
- If \(|A| = |B|\), then \( |A|^2 - |B|^2 = 0\).

Thus, the assertion that \((A + B) \cdot (A - B)\) is always positive is **false**.

### Step 4: Understanding the Reason
The reason states that the expression is positive if \(|A| > |B|\). We have already established that if \(|A| > |B|\), then \((A + B) \cdot (A - B) = |A|^2 - |B|^2 > 0\). This is indeed true.

### Conclusion
- The assertion is false because \((A + B) \cdot (A - B)\) is not always positive.
- The reason is true because the expression is positive when \(|A| > |B|\).

### Final Answer
The answer is: Assertion is false, but reason is true.

---