Vector definition

[Kamel Serend <kamel@nolimits-online.com>]

Hi Philippe,

A vector is a mathematical object. We usually represent it using a sort of arrow. A vector is
thus defined by its length (or magnitude), its direction (the line supporting it), and its
orientation (positive or negative compared with the progression of the line).
As you can imagine, if we note K a vector, the vector that is twice as long will be 2*K or 2K
in short. We say that the two vectors are colinear because they can define the same line. A
trick: K and -K are also colinear, even if they do not have the same orientation.
A vector is useful to define a line. all you need is then this vector and a point belonging to
the line.
A vector is defined also as two extremities A and B (for instance). A and B can be two points
in either 2D or 3D. The resulting vector will then have the following co-ordinates:
    K=AB=(xb-xa, yb-ya, zb-za) in the 3D vector/points case, and
    K=AB=(xb-xa, yb-ya) in the 2D vector/points one.

Apart from that, vectors are also used to compute angles between lines, or between lines and
planes (CF ray-tracing), we can also use them to define matrices as an association of vectors,
and positions (a point can be a vector with its origin in O(0,0,0)).
If you want any other information, let me know.

Kamel.

PHILIPPE NGUE wrote:

> Hi
> i don't know what's a vector?. I don't know anything about programming.
> i know how to use karel,beeper,wall,and turbo pascal,robotical that's the only thing i know
>
> So teach me.
>
> Thanks
>
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