Three vectors `vecA, vecB` and `vecC` satisfy the relation `vecA. vecB=0` and `vecA. vecC=0.` The vector `vecA` is parallel to

Options

A. `vecB and vecC`
B. `vecA xx vecB`
C. `vecB+vecC`
D. `vecBxxvecC`

Answer

To solve the problem, we need to analyze the given conditions regarding the vectors \(\vec{A}\), \(\vec{B}\), and \(\vec{C}\).

### Step-by-Step Solution:

1. **Understanding the Dot Product**:
We know that the dot product of two vectors \(\vec{A}\) and \(\vec{B}\) is given by:
\[ \vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos(\theta) \]
where \(\theta\) is the angle between the two vectors.

2. **Given Conditions**:
The problem states that:
\[ \vec{A} \cdot \vec{B} = 0 \quad \text{and} \quad \vec{A} \cdot \vec{C} = 0 \]
This implies that the angle \(\theta\) between \(\vec{A}\) and \(\vec{B}\) is \(90^\circ\) (since \(\cos(90^\circ) = 0\)), meaning \(\vec{A}\) is perpendicular to \(\vec{B}\).

3. **Analyzing the Second Condition**:
Similarly, since \(\vec{A} \cdot \vec{C} = 0\), it follows that \(\vec{A}\) is also perpendicular to \(\vec{C}\).

4. **Understanding the Relationship**:
Since \(\vec{A}\) is perpendicular to both \(\vec{B}\) and \(\vec{C}\), we can conclude that \(\vec{A}\) lies in a direction that is orthogonal to the plane formed by \(\vec{B}\) and \(\vec{C}\).

5. **Using the Cross Product**:
The vector that is perpendicular to both \(\vec{B}\) and \(\vec{C}\) can be represented by the cross product:
\[ \vec{A} \parallel \vec{B} \times \vec{C} \]
This means that \(\vec{A}\) is parallel to the vector resulting from the cross product of \(\vec{B}\) and \(\vec{C}\).

6. **Final Conclusion**:
Therefore, we conclude that:
\[ \vec{A} \text{ is parallel to } \vec{B} \times \vec{C} \]

### Answer:
\(\vec{A}\) is parallel to \(\vec{B} \times \vec{C}\).