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vectorial velocity

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Let's say I have a ball flying almost parallel with a wall (but will eventualy hit the wall). How can I find out the velocity of the ball on the direction perpendicular to the wall? I think I should break the direction of the ball into the components, but which components? In which system?

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Scale the wall's normal by the dot product of itself with the ball's velocity - to get the component velocity of the ball in the direction of the wall normal (note that the normal must have length 1 for this to work).

If you just want the speed you can just use the dot product value. Negative means you are moving towards the wall and positive away from it. 0 means you are moving parallel to the wall.

You can get the velocity component parallel to the wall by subtracting the vector you just calculated from the actual velocity.

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The components you want are those in the wall's local space. In particular, you need one of the axes to be the wall's normal (perpendicular to the wall's surface); it doesn't much matter what the other two (in the plane of the wall) are, generally.

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