A technique is proposed for object manipulation with a virtual tool using multiple exact interactions. Exact test is introduced that uses real-time collision detection for both hand-and-tool and tool-and-object interactions. Chopsticks are adopted for one of the trials of our technique; although they have a very simple shape, they do have multiple functions. Here, a virtual object is manipulated by the virtual chopsticks, which are used by the motion of a user's hand captured by a hand gesture input device. Exact interaction is applied between the hand and chopsticks based on correct table manners. Experimental results demonstrate the effectiveness of the proposed multiple exact interactions, especially for precise object alignment tasks.