# Find plane normal and origin from homogeneous matrix

Given a $3\times 4$ matrix how do I find the plane equation ?

My matrix is as follows: $$\left[ \matrix { a&b&c&d \\ e&f&g&h \\ i&j&k&l } \right]$$

Where $X_1=(a,b,c,d)$; $X_2=(e,f,g,h)$ and $X_3=(i,j,k,l)$ are $3$ distinct points expressed in homogeneous coordinates. Those $3$ points in space, define a plane such as $Ax + By + Cz + D = 0$, ($A, B, C, D$ constants not all zero). How do I find those $A,B,C,D$ values ?

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Are you working in $\mathbb R^4$? The points are telling that! –  Babak S. May 14 '13 at 12:12
No it's $\mathbb R^3$ –  malat May 14 '13 at 12:29
You're working in projective space, $\mathbb{RP}^3$. –  Rhys May 14 '13 at 13:13