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    Thanks for entering my thread, recently I have been contemplating the equation of a plane found by using 3 points. Suppose I have 3 position vectors (A,B & C) which all lie on the plane of which equation I am searching for, I can obtain the equation in two ways:
    Let R be a general point on the plane then OR = AR + OA
    AR= (Lamba)AB + (Mu)AC
    therefore equation of the plane is A + (Lamba)(B-A) + Mu(C-A)


    Finding AB & AC, then find the cross product (AB x AC) to get the normal vector to the plane, we can then use the dot product to find that (R-A).(AB x AC)=0 leading to:
    R.(AB x AC)= A.(AB x AC)

    I am unsure of what the differences between these equations are, but I know they are equations of the same plane, can someone please explain/send relative information.

    Also what are the uses of both equations? I know with 2nd I can convert to Cartesian form much easier.

    Many thanks for reading

    They're just different forms of the same thing. Just like how a line has a vector equation in parametric form, vector product form and Cartesian form. Just different ways of expressing the same thing. Sometimes different forms can be more useful depending on what you are trying to do.
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Updated: April 11, 2016
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