The correct response is:
a- the potential for the Chinese vote on the United Nations Security Council.
President Nixon believed that improved relations with China would lead to the potential for China's vote on the United Nations Security Council. This was one of the reasons behind his efforts to establish diplomatic relations with China in the early 1970s, which ultimately led to the normalization of relations between the United States and China.
Nixon saw China as a potential ally against the Soviet Union during the Cold War and believed that closer relations with China could provide strategic benefits for the United States, including increased influence in international organizations such as the United Nations.