Let `vecA` be a unit vecrtor along the axis of rotation of a purely rotating body and `vecB` be a unit vector along the velocity of a particle P of the body away from the axis. The value of `vecA.vecB` is

Options

A. 1
B. -1
C. 0
D. none of these

Answer

To solve the problem, we need to determine the value of the dot product \( \vec{A} \cdot \vec{B} \), where \( \vec{A} \) is a unit vector along the axis of rotation of a purely rotating body, and \( \vec{B} \) is a unit vector along the velocity of a particle \( P \) of the body, which is moving away from the axis.

### Step-by-Step Solution:

1. **Understanding the Vectors**:
- \( \vec{A} \) is a unit vector along the axis of rotation. This means it points directly along the axis and has a magnitude of 1.
- \( \vec{B} \) is a unit vector that represents the velocity of a particle \( P \) on the rotating body. This particle moves in a circular path around the axis of rotation.

2. **Visualizing the Geometry**:
- When a body rotates, any point on the body moves in a circular path. The velocity vector \( \vec{B} \) at any point on this circular path is tangent to the circle at that point.
- The axis of rotation (along \( \vec{A} \)) is perpendicular to the plane of motion of the particle \( P \).

3. **Finding the Angle Between Vectors**:
- Since \( \vec{A} \) points along the axis of rotation and \( \vec{B} \) is tangent to the circular path of the particle, the two vectors are perpendicular to each other.
- The angle \( \theta \) between \( \vec{A} \) and \( \vec{B} \) is \( 90^\circ \).

4. **Calculating the Dot Product**:
- The dot product of two vectors is given by the formula:
\[ \vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos(\theta) \]
- Since both \( \vec{A} \) and \( \vec{B} \) are unit vectors, their magnitudes are 1:
\[ |\vec{A}| = 1, \quad |\vec{B}| = 1 \]
- Therefore, the dot product simplifies to:
\[ \vec{A} \cdot \vec{B} = 1 \cdot 1 \cdot \cos(90^\circ) \]
- We know that \( \cos(90^\circ) = 0 \), so:
\[ \vec{A} \cdot \vec{B} = 0 \]

5. **Final Result**:
- The value of \( \vec{A} \cdot \vec{B} \) is \( 0 \).

### Conclusion:
Thus, the final answer is:
\[ \vec{A} \cdot \vec{B} = 0 \]