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QUESTION
Determine the vector equation of the plane which passes through
the point $P(-1,1,2)$ and has normal ${\bf i}-2{\bf j}+3{\bf k}$
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ANSWER
The equation of the plane is $\textbf{r.n}=c,$ i.e.
$\textbf{r}.(1,-2,3)=c.$ $P$ is on the plane therefore
$(-1,1,2).(1,-2,3)=-1-2+6=3=c$ so the equation of the plane is
$\textbf{r}.(1,-2,3)=3.$
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