Math: setting velocity to 0 along a specific angle

Hello all,

I have a math question for those of you who are gifted in the area. I can't find it through google because I am not sure how to ask the question.

Basically the problem is this: I have a physics object with velocity x,y. Because I need to know it's velocity relative to an arbitrary axis I calculate that and store it as Xg,Yg (it's based on the direction gravity is pulling where Yg relates to relative up/down). I calculate Xg,Yg based on polar projections using GravityAngle. Now here is what I need to do- I check Xg and if it is under a certain threshold I need to set it to zip, but the only way I can do that is by setting the objects velocity which is stored as x,y. what is the equation to alter the objects velocity in x,y such that Xg will be 0 and Yg will remain the same, and vica versa?

Thanks

I just realized if I can calculate arbitrary Xg,Yg from x,y based on angle of gravity then I can calculate x,y from Xg,Yg after making necessary changes. Do you think this is the best way to do it?

As it so happens I've been messing with such math lately. Calculating the velocity along an axis is a "vector projection" and looks like this:

velocity_along_angle = velocityX*cos(angle)+velocityY*sin(angle)

Thanks, I learned about rotation matrices and stuff today from an electrical engineer but this is a lot more simple. I need to learn this