Homogeneous plane containing a line and a point

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Say we have a line in Plucker coordinate {v|m} and a point $p$. I know that we can have a plane containing the ones with [vxp+m|-p*m], where $\times$ is a cross product and $*$ is a dot product.

I would like to know how this formula is derived.

It seems like the normal is the moment of the line around the point, but distance calculation meaning is eluding me.