If A.B =0 and `AxxB =1 ` , then A and B are

Options

A. perpendicular unit vectors
B. paraellel unit vector
C. parallel
D. anti - parallel

Explanation

To solve the problem, we need to analyze the given conditions: \( A \cdot B = 0 \) and \( A \times B = 1 \).

### Step 1: Analyze the dot product condition
The dot product \( A \cdot B = 0 \) indicates that the vectors \( A \) and \( B \) are perpendicular to each other. This is because the dot product of two vectors is given by:

\[ A \cdot B = |A| |B| \cos \theta \]

Where \( \theta \) is the angle between the two vectors. Since \( A \cdot B = 0 \), it implies that:

\[ \cos \theta = 0 \implies \theta = 90^\circ \]

### Step 2: Analyze the cross product condition
The cross product \( A \times B = 1 \) gives us information about the magnitudes of the vectors. The magnitude of the cross product is given by:

\[ |A \times B| = |A| |B| \sin \theta \]

Since we already established that \( \theta = 90^\circ \), we know that:

\[ \sin 90^\circ = 1 \]

Thus, we can simplify the equation to:

\[ |A \times B| = |A| |B| \cdot 1 = |A| |B| \]

Given that \( A \times B = 1 \), we have:

\[ |A| |B| = 1 \]

### Step 3: Conclusion about the vectors
From the above analysis, we conclude that \( A \) and \( B \) are perpendicular vectors (as established from the dot product) and their magnitudes multiply to 1 (as established from the cross product). This means that both \( A \) and \( B \) must be unit vectors.

Therefore, the final answer is that \( A \) and \( B \) are perpendicular unit vectors.

### Final Answer:
**A and B are perpendicular unit vectors.**

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