Answer
The work done by a force F in moving an object A to B is $\mathbf{F}\cdot \overrightarrow{AB}$.
Work Step by Step
Consider an object that moves from point A to B, but the force acting on the object is at an angle $\theta $.
The work done $W$ is defined as the product of the magnitude of the force F in the direction of displacement and the magnitude of the displacement.
The component of force $\mathbf{F}$ in the direction of displacement is,
$\mathbf{F}=\left\| \mathbf{F} \right\|\cos \theta $
The magnitude of the displacement vector is,
$\text{Magnitude of }\overrightarrow{AB}=\left\| \overrightarrow{AB} \right\|$
According to the definition of work-done. The work-done is,
$\begin{align}
& \text{W}=\left( \left\| \overrightarrow{AB} \right\| \right)\left( \left\| \mathbf{F} \right\|\cos \theta \right) \\
& =\left\| \overrightarrow{AB} \right\|\left\| \mathbf{F} \right\|\cos \theta \\
& =\mathbf{F}\centerdot \overrightarrow{AB}
\end{align}$
Hence, the work done by a force F in moving an object A to B is $\mathbf{F}\cdot \overrightarrow{AB}$.
