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Centripetal force is the force acting on an object moving in a circular path, directed towards the center of the circle around which the object is moving. This force is responsible for keeping the object in its circular path. If the centripetal force is removed, the object will no longer follow a circular path.

Let's analyze each option: a) If the object moves radially outward, it means the object would continue to move away from the center of the circular path. This is not correct, as there is no force acting to push the object away from the center once the centripetal force is removed. b) If the object moves radially inward, it means the object would continue to move towards the center of the circular path. This is also not correct, as there is no force acting on the object towards the center once the centripetal force is removed. c) If the object moves vertically downward, it means gravity would have a major influence on the object's motion. However, this option does not take into account the object's initial motion in the circular path, so it is not correct. d) If the object moves in the direction of its velocity vector at the instant the centripetal force vanishes, it means the object would continue to move in a straight line (tangential to the circular path) in the direction it was moving at the instant the force was removed. This is correct because, in the absence of centripetal force, the object will follow its initial linear velocity.

The correct option is (d). The object will move in the direction in which its velocity vector points at the instant the centripetal force vanishes.