# point below a plane

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 ?

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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.