1. ## Unit normal vector

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

2. ## Re: Unit normal vector

What are the three points?

3. ## Re: Unit normal vector

Three points determine a plane. Given three points, P, Q, and R, construct the two vectors $\vec{PQ}$ and $\vec{PR}$ that lie in that plane. The cross product of the two vectors is normal to the plane. If that normal vectors is $A\vec{i}+ B\vec{j}+ C\vec{k}$ and any one of the three points is $(x_0, y_0, z_0)$ then the eqation of the plane is $A(x- x_0)+ B(y- y_0)+ C(z- z_0)= 0$ and the unit normal vector is $\frac{1}{\sqrt{A^2+ B^2+ C^2}}\left(A\vec{i}+ B\vec{j}+ C\vec{k}\right)$.