If a and b are two unit vectors, then `a xx b` is a unit vector if .........

Answer

To determine the condition under which the cross product of two unit vectors \( \mathbf{a} \) and \( \mathbf{b} \) is also a unit vector, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Unit Vectors**:
- A unit vector has a magnitude of 1. Therefore, for the vectors \( \mathbf{a} \) and \( \mathbf{b} \):
\[ |\mathbf{a}| = 1 \quad \text{and} \quad |\mathbf{b}| = 1 \]

2. **Cross Product Magnitude**:
- The magnitude of the cross product of two vectors \( \mathbf{a} \) and \( \mathbf{b} \) is given by the formula:
\[ |\mathbf{a} \times \mathbf{b}| = |\mathbf{a}| |\mathbf{b}| \sin \theta \]
- Here, \( \theta \) is the angle between the two vectors \( \mathbf{a} \) and \( \mathbf{b} \).

3. **Substituting the Magnitudes**:
- Since both \( \mathbf{a} \) and \( \mathbf{b} \) are unit vectors, we substitute their magnitudes into the formula:
\[ |\mathbf{a} \times \mathbf{b}| = 1 \cdot 1 \cdot \sin \theta = \sin \theta \]

4. **Condition for Unit Vector**:
- For \( \mathbf{a} \times \mathbf{b} \) to also be a unit vector, its magnitude must equal 1:
\[ |\mathbf{a} \times \mathbf{b}| = 1 \]
- Therefore, we need:
\[ \sin \theta = 1 \]

5. **Finding the Angle**:
- The sine of an angle is equal to 1 when the angle \( \theta \) is:
\[ \theta = \frac{\pi}{2} \quad \text{(90 degrees)} \]

6. **Conclusion**:
- This implies that the vectors \( \mathbf{a} \) and \( \mathbf{b} \) must be perpendicular (orthogonal) to each other for their cross product \( \mathbf{a} \times \mathbf{b} \) to be a unit vector.

### Final Answer:
The cross product \( \mathbf{a} \times \mathbf{b} \) is a unit vector if \( \mathbf{a} \) and \( \mathbf{b} \) are perpendicular (orthogonal), i.e., \( \theta = \frac{\pi}{2} \).