The angle between two vectors `veca` and `vecb` is `pi//2`. Then `|hata xx hatb|` is

Options

A. zero
B. `ab sin theta`
C. `sin theta`
D. 1

Answer

To solve the problem, we need to find the magnitude of the cross product of two unit vectors \(\hat{a}\) and \(\hat{b}\), given that the angle between them is \(\frac{\pi}{2}\).

### Step-by-Step Solution:

1. **Understanding Unit Vectors**:
- The vectors \(\hat{a}\) and \(\hat{b}\) are unit vectors. This means that their magnitudes are both equal to 1:
\[ |\hat{a}| = 1 \quad \text{and} \quad |\hat{b}| = 1 \]

2. **Identifying the Angle**:
- The angle \(\theta\) between the two vectors is given as \(\frac{\pi}{2}\) (90 degrees).

3. **Using the Cross Product Formula**:
- The magnitude of the cross product of two vectors \(\vec{u}\) and \(\vec{v}\) is given by:
\[ |\vec{u} \times \vec{v}| = |\vec{u}| |\vec{v}| \sin(\theta) \]
- In our case, substituting \(\hat{a}\) and \(\hat{b}\) into the formula, we have:
\[ |\hat{a} \times \hat{b}| = |\hat{a}| |\hat{b}| \sin(\theta) \]

4. **Substituting Known Values**:
- Since both \(|\hat{a}|\) and \(|\hat{b}|\) are 1, and \(\theta = \frac{\pi}{2}\):
\[ |\hat{a} \times \hat{b}| = 1 \cdot 1 \cdot \sin\left(\frac{\pi}{2}\right) \]

5. **Calculating \(\sin\left(\frac{\pi}{2}\right)\)**:
- We know that:
\[ \sin\left(\frac{\pi}{2}\right) = 1 \]

6. **Final Calculation**:
- Therefore, substituting this value back into the equation gives:
\[ |\hat{a} \times \hat{b}| = 1 \cdot 1 \cdot 1 = 1 \]

### Conclusion:
The magnitude of the cross product \(|\hat{a} \times \hat{b}|\) is \(1\).

### Answer:
\[ |\hat{a} \times \hat{b}| = 1 \]