运用空间向量处理立体几何问题 ,可以减少辅助线的添加 ,避开一些复杂的空间想象 ,降低了解题难度 .但笔者在教学中发现同学们在进行空间向量的运算时常出现错误 .现举例剖析如下 ,供同学们借鉴与参考 .1　混淆向量的和 (差 )与向量的数量积例 1　已知a =( 2 ,- 1 ,5) ,b =( - The use of space vector to deal with three-dimensional geometric problems can reduce the number of auxiliary lines added, avoid some complicated spatial imaginations, and reduce the difficulty of understanding problems. However, the author found that students often make mistakes in the calculation of space vectors in the teaching. As follows, for the students to learn from and reference to. 1 The sum of the vector (difference) and the number of vectors of the example 1 is known as a = (2, -1, 5), b = (-