若A1,A2 ,… ,An -1,An 围成封闭折线 ,则有如下的向量恒等式A1A2 +A2 A3 +… +AnA1=0 ,本文举例说明该恒等式在解题中的应用 .例 1　证明余弦定理 :三角形中 ,a2 =b2+c2 - 2bccosA ,b2 =c2 +a2 - 2cacosB ,c2 =a2 +b2 - 2bccosC .图 1　例 1图证明　如图 1 ,在△ABC中 ,AB ,BC If A1, A2, ..., An -1, An enclose a closed polyline, then there is the following vector identity A1A2 + A2 A3 +... +AnA1 = 0. This article illustrates the application of the identity in solving a problem. Example 1 Proving a cosine Theorem: In the triangle, a2 = b2 + c2 - 2bccosA, b2 = c2 + a2 - 2cacosB, c2 = a2 + b2 - 2bccosC. Figure 1 Example 1 Figure proves that in Figure 1, in △ ABC, AB, BC