Vector3.Project() not working as expected?

Consider the following shitty image:

N is my normal, V is a point I am passing to Vector3.Project():

 Vector3 P = Vector3.Project(V, N);

The problem is that the result of P is where I show in the image, but I expected it to be somewhere along N.

I have thrown in Debug.DrawRay statements to ensure my point and normal are as I expect, and they are. Am I misunderstanding what Vector3.Project() does?

Depending on the direction of N, the result of P is different (sometimes closer, sometimes worse), but it is always incorrect.

What could I be doing wrong?

EDIT:

If I do this (where Np is the world position of the normal vector I care about):

 Vector3 P = Np + (N * Vector3.Distance(V, Np));

I get the desired result. So what is it that I am misunderstanding about Vector3.Project()? How would I use Vector3.Project() to get the same result as the above expression?