The moment of the force F acting at a point P, about the point C is

Options

A. `FtimesCP`
B. `CP*F`
C. a vector having the same direction as F
D. `CPtimesF`

Answer

To solve the problem of finding the moment of a force \( \mathbf{F} \) acting at a point \( P \) about the point \( C \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Moment of a Force**:
The moment of a force about a point is defined as the cross product of the position vector (from the point to the line of action of the force) and the force vector itself. Mathematically, it is given by:
\[ \mathbf{M} = \mathbf{r} \times \mathbf{F} \]
where \( \mathbf{M} \) is the moment, \( \mathbf{r} \) is the position vector, and \( \mathbf{F} \) is the force vector.

2. **Identify the Position Vector**:
In this case, we need to find the position vector \( \mathbf{r} \) from point \( C \) to point \( P \). This can be expressed as:
\[ \mathbf{r} = \mathbf{P} - \mathbf{C} \]
or equivalently,
\[ \mathbf{r} = \mathbf{CP} \]

3. **Substitute the Position Vector into the Moment Equation**:
Now, we can substitute \( \mathbf{r} \) into the moment equation:
\[ \mathbf{M} = (\mathbf{P} - \mathbf{C}) \times \mathbf{F} \]

4. **Final Expression for the Moment**:
The moment of the force \( \mathbf{F} \) acting at point \( P \) about point \( C \) is then given by:
\[ \mathbf{M} = \mathbf{CP} \times \mathbf{F} \]

5. **Conclusion**:
Therefore, the moment of the force \( \mathbf{F} \) acting at point \( P \) about point \( C \) is represented by the expression \( \mathbf{CP} \times \mathbf{F} \).