Normal of a 3D tangent

Question

So I have 3 points in a 3D space with a curve passing through the points. I have found the tangent of the point in the middle by averaging the two points either side of it, but I want to find the Normal at the point in the middle. How would I do this without knowing the equation of the line?

`P(1) = (0,1,0)
P(2) = (2,2,2)
p(3) = (4,4,4)

Tangent at P(2) = (4,3,4)`

Thanks!

Answer 1

A = P2 - P1 ... vector between 2 points on the curve (one is the middle point .. P2)

• normal = A x tangent
• but as MBo pointed out there are infinite number of normals (all are perpendicular to the curve lying on the same plane)
• above equation gives one perpendicular to curve and to that A vector