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Sorry if my post would be in the wrong section, but I didn't know where to put it as there's no topic called 'projective geometry'.

I'm working on the following problem. Suppose we're working in the projective space [tex]\mathbb{P}^4[/tex] where we have given the Plucker coordinates of a plane [tex] \alpha: (a_0:a_1:a_2:a_3)[/tex] and the Plucker coordinates of a line [tex]l = (d:m)=(d_1:d_2:d_3:m_1:m_2:m_3)[/tex]. The question is, what are the coordinates of the intersection point?

I can represent the plane [tex]\alpha[/tex] analytically as [tex]a_0x_0+a_1x_1+a_2x_2+a_3x_3=0[/tex] which can be useful to work with, but I also want an analytically expression of the line, which I cannot find. I did some research and I found on wikipedia that the coordinates of the intersection point are given by: [tex](x_0:x)=(a\cdot d: a \times m - a_0d)[/tex] where [tex]x=(x_1:x_2:x_3)[/tex] and [tex]a=(a_1:a_2:a_3)[/tex]. Honestly, I don't know how they came to that answer as I have no analytical expression for the line [tex]l[/tex].

How do I have to approach this problem?

Many thanks,

Impo