If a vector `vec(A)` is parallel to another vector `vec(B)` then the resultant of the vector `vec(A)xxvec(B)` will be equal to

Options

A. A
B. `vecA`
C. zero vector
D. zero

Explanation

To solve the problem, we need to analyze the relationship between two vectors, \(\vec{A}\) and \(\vec{B}\), that are parallel to each other. The question asks for the resultant of the cross product \(\vec{A} \times \vec{B}\).

### Step-by-Step Solution:

1. **Understanding Parallel Vectors**:
- When two vectors are parallel, it means they point in the same direction or in exactly opposite directions. Mathematically, if \(\vec{A}\) is parallel to \(\vec{B}\), the angle \(\theta\) between them is either \(0^\circ\) or \(180^\circ\).

2. **Cross Product Formula**:
- The cross product of two vectors \(\vec{A}\) and \(\vec{B}\) is given by the formula:
\[ \vec{A} \times \vec{B} = |\vec{A}| |\vec{B}| \sin(\theta) \hat{n} \]
where \(|\vec{A}|\) and \(|\vec{B}|\) are the magnitudes of the vectors, \(\theta\) is the angle between them, and \(\hat{n}\) is the unit vector perpendicular to the plane formed by \(\vec{A}\) and \(\vec{B}\).

3. **Substituting the Angle**:
- Since \(\vec{A}\) and \(\vec{B}\) are parallel, we can substitute \(\theta = 0^\circ\) (or \(180^\circ\)). In both cases, \(\sin(0^\circ) = 0\) and \(\sin(180^\circ) = 0\).

4. **Calculating the Cross Product**:
- Plugging in the value of \(\theta\):
\[ \vec{A} \times \vec{B} = |\vec{A}| |\vec{B}| \sin(0^\circ) \hat{n} = |\vec{A}| |\vec{B}| \cdot 0 \cdot \hat{n} = 0 \]
- Therefore, the cross product \(\vec{A} \times \vec{B}\) results in the zero vector.

5. **Conclusion**:
- The resultant of the vector \(\vec{A} \times \vec{B}\) is equal to the zero vector, denoted as \(\vec{0}\).

### Final Answer:
\[ \vec{A} \times \vec{B} = \vec{0} \quad \text{(zero vector)} \]