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由于向量具有几何与代数两个方面的特征,因此,在处理向量问题时容易混淆其几何与代数性质而造成错误,下面列举几种常见的错误。一、忽略向量夹角的范围致错例1若向量e1=(x,2x),e2=(-3x,2),且e1,e2的夹角为钝角,求x的取值范围。错解:因为e1,e2的夹角为钝角,所以e1·e2<0,即-3x2+4x<0,解得x<0或x>4/3,则x的取值范围是x<0或x>4/3.
Because the vector has the characteristics of two aspects of geometry and algebra, it is easy to confuse the geometry and algebraic properties and cause errors when dealing with vector problems. Here are some common errors. First, ignore the range of the included angle error. Example 1 If the vector e1 = (x, 2x), e2 = (-3x, 2), and the angle between e1, e2 is an obtuse angle, find the value range of x. Misunderstanding: Because the angles between e1 and e2 are obtuse angles, so e1·e2<0, that is -3x2+4x<0, and the solution is x<0 or x>4/3, the range of x is x<0. Or x>4/3.