If `|veca xx vecb| = ab` then the angle between `veca and vecb` is

Options

A. `pi//2`
B. `pi`
C. zero
D. any angle between zereo and `pi`

Answer

To solve the problem, we need to find the angle between the vectors \(\vec{a}\) and \(\vec{b}\) given that the magnitude of their cross product is equal to the product of their magnitudes.

### Step-by-Step Solution:

1. **Understand the Cross Product**:
The magnitude of the cross product of two vectors \(\vec{a}\) and \(\vec{b}\) is given by the formula:
\[ |\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin \theta \]
where \(\theta\) is the angle between the two vectors.

2. **Set Up the Equation**:
According to the problem, we have:
\[ |\vec{a} \times \vec{b}| = ab \]
where \(a = |\vec{a}|\) and \(b = |\vec{b}|\).

3. **Substitute the Magnitude of the Cross Product**:
Substitute the expression for the magnitude of the cross product into the equation:
\[ |\vec{a}| |\vec{b}| \sin \theta = ab \]

4. **Simplify the Equation**:
Since \(a = |\vec{a}|\) and \(b = |\vec{b}|\), we can rewrite the equation as:
\[ ab \sin \theta = ab \]

5. **Divide Both Sides by \(ab\)**:
Assuming \(ab \neq 0\), we can divide both sides by \(ab\):
\[ \sin \theta = 1 \]

6. **Find the Angle**:
The sine of an angle is equal to 1 when:
\[ \theta = 90^\circ \quad \text{or} \quad \theta = \frac{\pi}{2} \text{ radians} \]

### Conclusion:
The angle between the vectors \(\vec{a}\) and \(\vec{b}\) is:
\[ \theta = 90^\circ \]