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Question 360073: why cant you name a plane using 3 collinear points?
Found 2 solutions by Alan3354, Jk22:
Answer by Alan3354(69443)   (Show Source):
Answer by Jk22(389)  (Show Source):
You can put this solution on YOUR website! if 3 point are collinear they describe a line : A,B,C, then AB = a *BC
and AC = b*BC
the vector AB is a multiple of the vector BC, hence the dimension of span(AB,BC,AC) is 1 :
p*AB + q*BC + r*AC = pa*BC + q*BC + rb*BC = BC*(pa+rb+q)
a plan would need 2 linearly independent vectors.
This is true if working in euclidean geometry. On spherical geometry, 3 points are "collinear" would be translated to "on the same great circle".
In this case lines become great circle, but we cannot take the "disk" as describing a plan, since in were in the embedding space.
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