Results 1 to 4 of 4

Math Help - scalar product

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    2

    scalar product

    Hi,

    I know HOW to use a scalar product. However I don't know why do we need it and need a image of the result.

    thanks,

    Vinh
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,904
    Thanks
    765
    Hello, vinh48!

    I know HOW to use a scalar product.
    However I don't know why do we need it and need a image of the result.

    As far as I know, the scalar product has no immediate meaning or image,
    . . but it is used in a variety of formulas.


    Given two vectors: . \vec u\text{ and }\vec v

    . . [1]\;\;\vec u \perp \vec v \:\text{ if and only if }\:\vec u\cdot\vec v

    . . [2]\;\;\text{The angle between }\vec u\text{ and }\vec v\text{ is given by: }\cos\theta \:=\:\frac{\vec u\cdot\vec v}{|\vec u||\vec v|}

    . . [3]\;\;\text{The projection of }\vec u\text{ onto }\vec v\text{ is: }\;\text{proj}_{\vec v}\vec u \;=\;\frac{\vec u \cdot\vec v}{|\vec v|^2}\,\vec v


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    I suggest that the scalar product is "similar" to a determinant.

    A determinant has a value which, by itself, is meaningless.
    However, it can be used in a variety of ways (e.g. Cramer's rule)
    . . for a number of mathematical tasks.

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2008
    Posts
    2
    Thanks Soroban for your quick reply.
    Yes, you just answered for the immediate meaning or image.

    It is use if we want to have a projection of a vector on another one.
    Can be use to calculate the shadow.

    Vinh
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by vinh48 View Post
    Hi,

    I know HOW to use a scalar product. However I don't know why do we need it and need a image of the result.

    thanks,

    Vinh
    It has numerous applications in physics. You can spend hours researching this. One basic application is calculating the work done by a force.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: September 7th 2010, 10:03 PM
  2. Scalar Product
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 3rd 2010, 02:06 PM
  3. multivariable differential for inner product(scalar product)?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 23rd 2009, 06:40 PM
  4. Dot and Scalar Product
    Posted in the Advanced Applied Math Forum
    Replies: 8
    Last Post: September 9th 2008, 09:03 PM
  5. Triple Scalar Product
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 9th 2008, 01:07 PM

Search Tags


/mathhelpforum @mathhelpforum