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Uzayda herhangi 3'ü doğrusal olmayan 5 doğru ve 5 nokta kaç düzlem belirtir?

Bu soruyu http://mathforum.org sitesindeki Ask Dr.Math bölümüne de yollamıştım ve hem oradan gelen aşağıdaki cevaptan (many Thanks to Dr. Tom) hem de http://answers.yahoo.com/question/index?qid=20100804132824AAzwvM2 adresindeki açıklamalardan anlayabildiğime göre;

Noktaların dördü (veya hepsi) aynı düzlem içinde değilse her üçlü nokta grubu bir düzlem meydana getireceğinden C(5, 3) = 10 düzlem,

Doğrular paralel değilse, o noktalardan geçmiyorlarsa ve birbirleriyle de kesişmiyorlarsa (bir nokta ve bir doğru, bir düzlem oluşturduğundan) 5·5 = 25 düzlem olmak üzere toplam 35 düzlem oluşuyor diye düşünüyorum.

Dr. Tom'dan gelen açıklamalar:

Generally, problems like this (in English, at least) refer to points or lines as being in "general position," meaning that there is nothing special about them, so five points, in general position, would be such that no three are in a line, no four are on a plane. In your translation, it could be that all five lie on the same plane, so only one plane would be determined by all the points.

Anyway, if the points are in general position, then any three points will determine a unique plane since otherwise, more than three will be on the same plane, or three will be on a line or something. If the 5 points are in general position, you are right: there are C(5,3) planes determined.

Similar things can be said about the lines. I assume also that they are in "general position" with respect to each other and to the point. In other words, the lines aren't parallel, don't pass through points, and don't pass through each other. If that's the case, there are 5*5 planes determined by every line/plane combination.

Lines "in general position" do not meet in space, and they're not parallel, either, so no planes will contain two or more lines.