vector question

[badescuga]

i have an object and a 3d direction vector and position for it . I would like to know how do i determine if a certain point X is in the space below the plan determined by my direction ?

Here is an image that i have drawn to make it more clear . In this image i've made the vector 2d

http://yfrog.com/53imgukp

Please Help!


Regards,
Aleandru Badescu

[HallsofIvy]

Do you mean a "plane" or a "line"?

A single vector determines a line, Ax+ By= C, in two dimensions. A point (x,y) is on that line if y= (C- Ax)/B. It is "below" that line if y< (C- Ax)/B. If B is positive (and you can always arrange for B to be positive by multiplying the entire equation by -1 if necesary) that is the same as Ax+ By< C.

In three dimensions, a single vector <A, B, C>, determines a plane Ax+ By+ Cz< D. (x, y, z) is "below" that line if z< (D- Ax- By)/C. Again, if C is positive, that is the same as Ax+ By+ Cz< D.