Good morning,
Given 3 points, I must find the unit normal vector for the best fit plane through them. The plane must also include the origin (0,0,0)
Can someone give me a hand?
Kind regards,
Kepler
Three points determine a plane. Given three points, P, Q, and R, construct the two vectors $\displaystyle \vec{PQ}$ and $\displaystyle \vec{PR}$ that lie in that plane. The cross product of the two vectors is normal to the plane. If that normal vectors is $\displaystyle A\vec{i}+ B\vec{j}+ C\vec{k}$ and any one of the three points is $\displaystyle (x_0, y_0, z_0)$ then the eqation of the plane is $\displaystyle A(x- x_0)+ B(y- y_0)+ C(z- z_0)= 0$ and the unit normal vector is $\displaystyle \frac{1}{\sqrt{A^2+ B^2+ C^2}}\left(A\vec{i}+ B\vec{j}+ C\vec{k}\right)$.