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collision detection rsponse btw balls

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Hi , I want to know how to detect collisions between two spheres.I know that collision occurs when d=(R+r) d is distance and R,r are radiuses.But I have many number of balls together and only one ball moves and remaining are fixed.Do i need to find distance between ball and every other ball at a moment??How to detect the point of collision or angle so i need to calculate the velocity and direction in which the ball moves???

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