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All those plane equations are confusing me so much Is it the same when it says to write an equation of plane that contains two points and, is determined by two points ? (I am assuming that a vector is given aswell , because I think its not possible to write equation of plane if just 2 points are given )

Johnny Adams
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    two points is not enough to define a plane, there should be something else given, i.e. a line or another point – Vasili Jan 09 '18 at 19:06
  • It might be a pencil of planes through a line. – Bernard Jan 09 '18 at 19:11
  • What vector? Normal vector to the plane or a vector lying on the plane? – GNUSupporter 8964民主女神 地下教會 Jan 09 '18 at 19:19
  • what about a vector lying on the plane ? – Johnny Adams Jan 09 '18 at 19:24
  • is it the same if it says for example a plane is determined by 3 points and a plane contains 3 points ? (do you write the equation in the same way )? – Johnny Adams Jan 09 '18 at 19:26
  • If there is no context that says otherwise, then you are correct, the phrase "the plane determined by the 3 points $A, B, C$" will mean "the plane passing through the 3 points $A, B, C$". However, in certain contexts the author may be referring to other means of defining planes. In that case "determined by" means whatever method the author is currently talking about. – Paul Sinclair Jan 10 '18 at 01:32

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