If a,b are the magnitudes of vectors `veca` & `vecb` and `veca.vecb=0` the value of `|vecaxxvecb|` is

Options

A. `0`
B. `ab`
C. `sqrt(ab)`
D. `a//b`

Answer

To solve the problem, we need to find the value of the magnitude of the cross product of two vectors \(\vec{a}\) and \(\vec{b}\) given that their dot product is zero.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We are given that the magnitudes of the vectors \(\vec{a}\) and \(\vec{b}\) are \(a\) and \(b\) respectively.
- We know that \(\vec{a} \cdot \vec{b} = 0\).

2. **Interpreting the Dot Product**:
- The dot product of two vectors is given by the formula:
\[ \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos(\theta) \]
where \(\theta\) is the angle between the two vectors.
- Since \(\vec{a} \cdot \vec{b} = 0\), it implies that:
\[ |\vec{a}| |\vec{b}| \cos(\theta) = 0 \]
- For this equation to hold true, either \(|\vec{a}| = 0\), \(|\vec{b}| = 0\), or \(\cos(\theta) = 0\). Since we are dealing with non-zero vectors, we conclude that:
\[ \cos(\theta) = 0 \implies \theta = 90^\circ \]
- This means the vectors \(\vec{a}\) and \(\vec{b}\) are perpendicular to each other.

3. **Finding the Cross Product**:
- The magnitude of the cross product of two vectors is given by the formula:
\[ |\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin(\theta) \]
- Since we have established that \(\theta = 90^\circ\), we can substitute this into the equation:
\[ |\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin(90^\circ) \]
- We know that \(\sin(90^\circ) = 1\), so we have:
\[ |\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \cdot 1 = |\vec{a}| |\vec{b}| \]
- Substituting the magnitudes \(a\) and \(b\):
\[ |\vec{a} \times \vec{b}| = a \cdot b \]

4. **Conclusion**:
- Therefore, the value of \(|\vec{a} \times \vec{b}|\) is \(ab\).

### Final Answer:
\[ |\vec{a} \times \vec{b}| = ab \]