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苏教版高中数学必修4第二章的“2.2.3向量的数乘”小节中,有这样的例题:例如图1,△OAB中,C为直线AB上一点,AC=λCB(λ≠-1).求证:OC=(OA+λOB)/(1+λ).例题结论OC=(OA+λOB)/(1+λ)表明:当点O不在直线AB上时,起点为O,终点为直线AB上一点C(C不与B重合)的向量OC可以用OA,OB表示.配套的教参指出:当λ∈R且λ≠-1时,OC=(OA+λOB)/(1+λ)是线段定比分点的向量公式.虽然上述向量公式许多高中数学教材都有所涉及,但通常只是作为一种结果呈现.教学中笔者发现,充分揭示该向量公式的几何意义,对于学生更好地理解与灵活应用向量可起到促进作用.下
For example, in Figure 1, △ OAB, C is the last point of AB, AC = λCB (λ ≠ -1). Proof: OC = (OA + λOB) / (1 + λ) Example Conclusion OC = (OA + λOB) / (1 + λ) shows that when the point O is not on the straight line AB, , And the ending point is the vector OC at the point AB on the straight line AB (where C does not coincide with B), which can be expressed as OA and OB. The accompanying teaching reference states that OC = (OA + λOB) / (1 + λ) is the vector formula of the line segment’s definite score point.Although many senior high school mathematics teaching materials mentioned above are involved in the vector formula, they are usually just presented as a result.The teaching of the author found that fully revealing the geometric meaning of the vector formula, For students to better understand and flexible application of vector can play a catalytic role