A vectors `vecr` satisfies the equations `vecr xx veca=vecb` and `vecr*veca=0`. Then

Options

A. `vecr= (veca xx vecb)/(veca*vecb)`
B. `vecr= (veca xx vecb)/(veca*veca)`
C. `vecr= (veca xx vecb)/(vecb*vecb)`
D. none of these

Explanation

To solve the problem, we need to analyze the given equations involving the vector \(\vec{r}\):

1. **Given Equations**:
- \(\vec{r} \times \vec{a} = \vec{b}\)
- \(\vec{r} \cdot \vec{a} = 0\)

2. **Understanding the Equations**:
- The equation \(\vec{r} \times \vec{a} = \vec{b}\) indicates that \(\vec{b}\) is perpendicular to both \(\vec{r}\) and \(\vec{a}\) since the cross product of two vectors results in a vector that is orthogonal to both.
- The equation \(\vec{r} \cdot \vec{a} = 0\) indicates that \(\vec{r}\) is also perpendicular to \(\vec{a}\).

3. **Finding the Relationship**:
- Since \(\vec{r}\) is perpendicular to \(\vec{a}\), we can express \(\vec{r}\) in terms of \(\vec{b}\) and \(\vec{a}\).
- We can use the identity for the cross product:
\[ \vec{b} = \vec{r} \times \vec{a} \]
- Rearranging gives us:
\[ \vec{r} = \frac{\vec{b} \times \vec{a}}{|\vec{a}|^2} \]

4. **Conclusion**:
- Thus, we can express \(\vec{r}\) in terms of \(\vec{b}\) and \(\vec{a}\) as:
\[ \vec{r} = \frac{\vec{b} \times \vec{a}}{|\vec{a}|^2} \]

5. **Final Result**:
- The correct option based on the above derivation is option (b).