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Math Help - dot product/scalar product

  1. #1
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    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..

    can someone please explain
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  2. #2
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    Quote Originally Posted by metlx View Post
    I'd like to know why do we need the scalar product.. is there any practical use of it?
    Are you asking about a dot product?
    If not, what do you mean by scalar product?
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  3. #3
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    <br />
\vec a  \cdot \vec b = |\vec a| |\vec b| \cdot cos \phi<br /> <br />

    ^that's what i mean
    isn't scalar product the same as dot product?
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  4. #4
    Senior Member Twig's Avatar
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    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,  \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  \mathbb{R}^{n} are orthogonal. That is, two vectors u and v are orthogonal if  \vec{u} \bullet \vec{v} = \sum_{i=1}^{n} u_{i}\cdot v_{i} = 0
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