I have provided an example below on how you could achieve the result that you are looking for. I hope this example helps.
Example:
In the example below I created a plane at the world origin. The normal for this plane is straight up (0,0,1), I then passed in the vector that I wanted to be projected on to the plane (the red debug line). I then provided the result as the end point for second debug line (green).
Make it a great day