How to calculate the equation of a plane passing through three points?
To find the equation of a plane passing through three given points in 3D, let the three points be A(x
1
, y
1
, z
1
), B(x
2
, y
2
, z
2
), and C(x
3
, y
3
, z
3
). First, calculate two vectors lying in the plane, say
AB
= (x
2
- x
1
, y
2
- y
1
, z
2
- z
1
) and
AC
= (x
3
- x
1
, y
3
- y
1
, z
3
- z
1
). Then, find the cross product of these vectors to get the normal vector n to the plane.
The equation of the plane is then given by:
n · (r - r ? ) = 0
where r is a point on the plane, (r - r ? ) is a known point (such as A ), and n is the normal vector obtained from the cross-product.
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