Check the determinant.yecko said:
The equation for a plane containing 3 points is determined using the point-normal form, which is:
(x - x1)a + (y - y1)b + (z - z1)c = 0
where (x1, y1, z1) is one of the given points and (a, b, c) is the normal vector of the plane.
To find the normal vector of a plane from 3 points, you can use the cross product of two vectors formed by the given points. The resulting vector will be perpendicular to the plane and can be used as the normal vector in the point-normal form of the plane equation.
No, the 3 points must be non-collinear, meaning they cannot all lie on the same line. If the points are collinear, there are an infinite number of planes that could contain them, so an equation cannot be determined.
No, at least 3 non-collinear points are required to uniquely determine a plane. With only 2 points, there are an infinite number of planes that could contain them, so an equation cannot be determined.
No, the distance formula is used to calculate the distance between two points, but it cannot be used to find an equation for a plane. The point-normal form or the standard form of the plane equation should be used instead.