Dot Product/Examples/Work Done

Examples of Dot Product

Let $\mathbf F$ represent a force acting on a body $B$.

Let $\mathbf d$ denote the displacement effected on $B$ by $\mathbf F$.

Then the work done by $\mathbf F$ on $B$ is given by:

$W = \mathbf F \cdot \mathbf d = \norm {\mathbf F} \norm {\mathbf d} \cos \theta$

where:

$\cdot$ denotes dot product

$\theta$ is the angle between the directions of $\mathbf F$ and $\mathbf d$.

Sources

• 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {II}$: The Products of Vectors: $1$. General