Assertion - If `theta` be the angle between A and B then
`tantherta (AxxB)/(AB)`
Reason - `AxxB` is perpendicular to AB.

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 both Assertion and Reason are false.

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 if θ is the angle between vectors A and B, then:
\[ \tan \theta = \frac{A \times B}{AB} \]
Here, \(A \times B\) represents the cross product of vectors A and B, and \(AB\) represents the product of the magnitudes of A and B.

2. **Cross Product Formula**: The cross product of two vectors A and B can be expressed as:
\[ A \times B = |A||B| \sin \theta \, \hat{n} \]
where \(\hat{n}\) is the unit vector perpendicular to the plane formed by A and B.

3. **Magnitude of Cross Product**: The magnitude of the cross product is given by:
\[ |A \times B| = |A||B| \sin \theta \]

4. **Substituting into the Assertion**: If we substitute the magnitude of the cross product into the assertion:
\[ \tan \theta = \frac{|A \times B|}{AB} = \frac{|A||B| \sin \theta}{|A||B|} = \sin \theta \]
This shows that the assertion is incorrect because \(\tan \theta\) is not equal to \(\sin \theta\).

5. **Understanding the Reason**: The reason states that \(A \times B\) is perpendicular to \(AB\). However, the correct statement is that the vector \(A \times B\) is perpendicular to both A and B, not to the line segment connecting A and B.

6. **Conclusion**: Since both the assertion and the reason are incorrect, we conclude that:
- The assertion is false.
- The reason is also false.

### Final Answer:
The correct option is **D**: Both assertion and reason are false.