Let `vecA` be a unit vector 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 find the value of the dot product of two unit vectors: \(\vec{A}\), which is along the axis of rotation of a purely rotating body, and \(\vec{B}\), which is along the velocity of a particle \(P\) of the body away from the axis.

### Step-by-Step Solution:

1. **Understanding the Vectors**:
- \(\vec{A}\) is a unit vector along the axis of rotation. By definition, a unit vector has a magnitude of 1.
- \(\vec{B}\) is a unit vector along the velocity of a particle \(P\) that is moving away from the axis of rotation. This vector is also a unit vector, meaning its magnitude is also 1.

2. **Identifying the Relationship between the Vectors**:
- In a rotating body, the velocity vector \(\vec{B}\) of a point \(P\) is always perpendicular to the radius vector \(\vec{r}\) that extends from the axis of rotation to the point \(P\).
- Since \(\vec{A}\) is along the axis of rotation, it is perpendicular to any radius vector \(\vec{r}\) in the plane of rotation.

3. **Determining the Angle Between the Vectors**:
- The angle \(\theta\) between \(\vec{A}\) and \(\vec{B}\) is \(90^\circ\) because \(\vec{A}\) (along the axis) and \(\vec{B}\) (along the velocity) are perpendicular to each other.

4. **Calculating the Dot Product**:
- The dot product of two vectors \(\vec{A}\) and \(\vec{B}\) 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:
\[ \vec{A} \cdot \vec{B} = 1 \cdot 1 \cdot 0 = 0 \]

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

### Final Answer:
\[ \vec{A} \cdot \vec{B} = 0 \]