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in R3 (3d) , having a vector perpendicular with a plane ( so we know where is 'up') , how do we determine if a certain point is below our plane ?

Regards, Alexandru Badescu

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Isn't this the same as your question vector question? Take the dot product of the perpendicular and the coordinates of the point. If it is less than zero, the point is below the plane.

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  • $\begingroup$ it is the same but the answer didn't quite work .. i guess i might have lost myseft in the details. $\endgroup$ – Alex Oct 26 '10 at 16:07
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If $v$ is the vector that points 'up' and $p_0$ is some point on your plane, and finally $p$ is the point that might be below the plane, compute the dot product $v \cdot (p-p_0)$. This projects the vector to $p$ on the up-direction. This product is $\lbrace -, 0, + \rbrace$ if $p$ is below, on, above the plane, respectively.

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