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
FP3 Vector plane equations help
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