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(3) Take any unit pure quaternion $n$ ($n^2=-1$) and consider
the plane $\Pi$ through the origin in ${\bf R^3}$ with normal
vector $n$. Then the plane $\Pi$ has equation $a x + b y + c z = 0
= v\cdot n$.
If $u_0$ is a point on the plane $\Pi$ then $u_0\cdot n =0$
and the points $u_0+ t n$ and $u_0 - t n$ are reflections of each
other in the plane.
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