## Problem on finding a plane from three points

Find the plane containing the points $(a,0,0)$, $(0, b, 0)$, and $(0,0,c)$.
• ## Solution

Recall that:
Because the plane goes through $(a, 0, 0)$, we choose $\bfx_0 = (a, 0, 0)$.
Now, we seek a normal vector $\bfn$.
Because $\bfn$ is a normal vector, it is perpendicular to any vector along the plane.
In particular, it is perpendicular to the vectors from $(a,0,0)$ to $(0,b,0)$ and from $(a,0,0)$ to $(0,0,c)$.
Recall that
Hence, the plane is given as $(bc, ac, ab) \cdot \bfx = abc$.