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

### Step 1: Understand the Concept of Moment
The moment of a force about a point is defined as the vector product (cross product) of the position vector and the force vector. The formula for the moment \( \mathbf{M} \) is given by:
\[ \mathbf{M} = \mathbf{r} \times \mathbf{F} \]
where \( \mathbf{r} \) is the position vector from point \( C \) to point \( P \).

### Step 2: Define the Position Vector \( \mathbf{r} \)
The position vector \( \mathbf{r} \) can be expressed in terms of the position vectors of points \( P \) and \( C \):
\[ \mathbf{r} = \mathbf{P} - \mathbf{C} \]
This means that \( \mathbf{r} \) is the vector that points from \( C \) to \( P \).

### Step 3: Substitute \( \mathbf{r} \) into the Moment Formula
Now, we substitute \( \mathbf{r} \) into the moment formula:
\[ \mathbf{M} = (\mathbf{P} - \mathbf{C}) \times \mathbf{F} \]

### Step 4: Calculate the Moment
The moment \( \mathbf{M} \) can now be calculated using the cross product:
\[ \mathbf{M} = \mathbf{P} \times \mathbf{F} - \mathbf{C} \times \mathbf{F} \]
This expression gives us the moment of the force about point \( C \).

### Step 5: Analyze the Direction of the Moment
The direction of the moment vector \( \mathbf{M} \) is perpendicular to the plane formed by \( \mathbf{r} \) and \( \mathbf{F} \). Therefore, the moment will not be in the same direction as \( \mathbf{F} \) or \( \mathbf{C} \).

### Conclusion
Thus, the moment of the force \( \mathbf{F} \) acting at point \( P \) about point \( C \) is given by:
\[ \mathbf{M} = (\mathbf{P} - \mathbf{C}) \times \mathbf{F} \]