1. ## dot product/scalar product

I'd like to know why do we need the scalar product.. is there any practical use of it?

In all the books I looked there's only a definition of a scalar product but it does not explain what its for and where can we use it..

2. Originally Posted by metlx
I'd like to know why do we need the scalar product.. is there any practical use of it?
If not, what do you mean by scalar product?

3. $\displaystyle \vec a \cdot \vec b = |\vec a| |\vec b| \cdot cos \phi$

^that's what i mean
isn't scalar product the same as dot product?

4. Hi

We can use it to calculate the work done by a force on a particle when it moves through a force field for example. Or you use it to break up forces into composants etc.

For example, $\displaystyle \int \vec{F} \bullet d\vec{r}$ is an integral of the first mentioned example above. Note that we have the dot product in the integral.

We also use it for example to determine if two vectors in $\displaystyle \mathbb{R}^{n}$ are orthogonal. That is, two vectors u and v are orthogonal if $\displaystyle \vec{u} \bullet \vec{v} = \sum_{i=1}^{n} u_{i}\cdot v_{i} = 0$