Please forgive the vague title, but I'm not asking to solve something. I was looking at the following question on calculating the work done by a force:
Calculate the work done by a force $\space \underline F \space$ of $ \space 12N \space$ whose line of action is parallel to $\space 2\underline {\hat i} + 3\underline {\hat j} - 2\underline {\hat k} \space$ when it moves its point of application through a displacement $\space \underline d \space$ of $\space 4m \space$ in a direction parallel to $\space -2\underline {\hat i} + \underline {\hat j} - 3\underline {\hat k} \space$.
We learnt how to calculate the work done; I can do that no problem. But can someone please shed light as to what exactly is going on here (in the question)?
What is the line of action?
What is the point of application?
I know this sounds dumb. But I love figuring out where such questions can be applied. But the choice of words prevent me from doing so.
Think about this. Work on an object is done only by the component of force parallel to the direction of motion. This is seen in the two-dimensional formula
$$ W = |F| \cos \theta $$
where $\theta$ is the angle between the force and the horizontal. We extend this to a line integral over the path $\gamma$ now:
$$ W = \int_{\gamma} \mathbf{F} \cdot \ d\mathbf{r} $$
in which this is just obtained by approximation. The line of action is the direction in which you wish to move your object, and the point of application is just that - where you're applying the force.