99 - The Unit Normal Vector
But what even is the unit normal vector?
An unit vector is a vector of magnitude(length) 1.
A normal vector to some curve or graph is a vector always perpendicular(orthogonal) to the curve at any point. As a dot product with another vector, it takes into account only the perpendicular part of that vector.
When we take the derivative of a parametric function we get a tangent vector to the curve. We need to make sure the function is parametrized though.
A vector tangent to a point is always perpendicular to another perpendicular vector through some line this point would be part of, and so we can rotate this tangent vector by 90 degrees to get our normal vector.
The quickest way to do this is swap the two components and make one of them negative.
Dividing a vector by its magnitude yields a vector of the same direction but magnitude 1.