I did a bit of reading and I figured out that equation of an hyperplane can be figured using a vector normal to the hyperplane and a point lying of the hyperplane (Am just extending the 3 D planar theory). Since given that, in our case the plane passes through origin, if I can find a vector normal to the plane, say \begin{displaymath} {\vec(n)} = a1*{\vec(i1)} + a2*{\vec(i2)} + ......, + an*{\vec(in)} \end{displaymath}, then the equation of the plan would be \begin{displaymath} a1*{\vec(i1)} + a2*{\vec(i2)} + ......, + an*{\vec(in)} = 0 \end{displaymath}

How correct or wrong am I ?