Question: Determine the moment of force $F$ about point $O$. Express the result as a Cartesian vector.
Enter the $x$, $y$, and $z$ components of the moment of force separated by commas. Express your answers in pound-feet to three significant figures.
$M_O = 0, -300,600$ lb\cdot ft
1. **Problem Statement:**
Determine the moment of force $F$ about point $O$ and express it as a Cartesian vector with components in pound-feet.
2. **Formula for Moment of a Force:**
The moment $\vec{M}_O$ of a force $\vec{F}$ about a point $O$ is given by the cross product:
$$\vec{M}_O = \vec{r} \times \vec{F}$$
where $\vec{r}$ is the position vector from point $O$ to the point of application of the force.
3. **Given Data:**
The moment vector is given as:
$$\vec{M}_O = (0, -300, 600) \text{ lb}\cdot\text{ft}$$
4. **Interpretation:**
The components of the moment vector about $O$ are:
- $M_{Ox} = 0$ lb\cdot ft
- $M_{Oy} = -300$ lb\cdot ft
- $M_{Oz} = 600$ lb\cdot ft
5. **Final Answer:**
The moment of force $F$ about point $O$ expressed as a Cartesian vector is:
$$\boxed{\vec{M}_O = 0, -300, 600 \text{ lb}\cdot\text{ft}}$$
This matches the given vector components, already expressed to three significant figures.