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I was wondering if someone could help me with the following question. Considering 3 lines L1, L2, L3 in P4 that do not pairwise intersect and are not all contained in any hyperplane. How can I calculate $dim(<L1,L2>\cap\ L3)$?

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  • $\begingroup$ What is $\langle L_1, L_2 \rangle$? And what do you mean by "dimension"? Notice that you are in a projective, not in a linear space. $\endgroup$ – Alex M. Mar 30 '17 at 17:03
  • $\begingroup$ It is the collection of all lines that intersect with both L1 and L2 $\endgroup$ – user133993 Mar 30 '17 at 20:23
  • $\begingroup$ The first step i have taken is to write $\textrm{dim}(\langle L_1,L_2\rangle \cap L_3) = \textrm{dim} \langle L_1,L_2\rangle + \textrm{dim}(L_3) - \textrm{dim}\langle L_1,L_2,L_3\rangle$ but then I don't really know how to progress from here $\endgroup$ – user133993 Mar 30 '17 at 20:30

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