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Exercise review: perpendicular-to-plane line

I have a plane in affine space in $\Bbb R^4$ described by two following equations:

\begin{Bmatrix}x+y-2z+q +2=0\\ -x-2y+3z+q=0\end{Bmatrix}

I have the coords of a point $P$: (1,2,3,4).

I have to describe the locus of all points $Q$ such that line $PQ$ is $\bot$ to the plane.

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    Dear @Willie, thanks for removing the off-topic comments.2012-06-29

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