Three points to normal notation (interpret the math)

Question

From: Euclidian Space: Planes, I see the formula:

Convert Three points to normal notation

N = (p1-p0) × (p2 - p0)

d = -N • p0^2

where:

N = normal to plane (not necessarily unit length) d = perpendicular distance of plane from origin. p0,p1 and p2 = vertex points x = cross product

When calculating the distance to the origin from the plane (d)... A) how is the p0 squared? B) how do I resolve the dot product of the vector (-N dot p0^2) to scalar distance?

Answer 1

Thanks to @DMGregory, I think I have it.

n = (p1 - p0).cross(p2 - p0);
n = normalize(n);
d = n.dot(p0);

Where p0, p1 and p2 are points. n is the (unit) normal vector and d is the distance to the origin from the plane.