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
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: .$\displaystyle \vec u\text{ and }\vec v$
. . $\displaystyle [1]\;\;\vec u \perp \vec v \:\text{ if and only if }\:\vec u\cdot\vec v$
. . $\displaystyle [2]\;\;\text{The angle between }\vec u\text{ and }\vec v\text{ is given by: }\cos\theta \:=\:\frac{\vec u\cdot\vec v}{|\vec u||\vec v|}$
. . $\displaystyle [3]\;\;\text{The projection of }\vec u\text{ onto }\vec v\text{ is: }\;\text{proj}_{\vec v}\vec u \;=\;\frac{\vec u \cdot\vec v}{|\vec v|^2}\,\vec v$
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
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.