[HELP] Arichmetic problem in 3d space

Hello guys ... i came here with this problem,


i have the dots G - C - T where....
C is the center of the cirunference
T is a random point inside the circunference
G is another random point inside the circunference.

I want to get the PQ vector3 where , PQ is a Proyection of CT over the semi rect R with origin in G parallel to vector(CT) and with the same direction.

My question is... how i cant get this?

 

Untested, just from the head:

CT = T - C
GC = C - G
P = G + Vector3.Project(GC, CT)
Q = P + CT