向量具有数字化的形式,同时又具有形象化的特征,故成为联系多项数学知识的媒介.一、与代数的交汇【例1】设实数x、y、z、a、b、c满足条件:(x2+y2+z2)(a2+b2+c2)=(ax+by+cz)2,求证ax=by=cz.证明:设m=(x,y,z),n=(a,b,c),且m与n的夹角为θ.∵m·n=｜m｜·｜n｜cosθ,m·n=ax+by+cz Vectors have a digitized form, but at the same time they have visualized features. Therefore, they have become a medium for connecting many mathematical knowledge. First, the intersection with algebra [Example 1] Set the real numbers x, y, z, a, b, and c to satisfy the conditions: (x2+y2+z2)(a2+b2+c2)=(ax+by+cz)2, verify ax=by=cz. Proof: Let m=(x,y,z),n=(a,b ,c), and the angle between m and n is θ.∵m·n=|m|·|n|cosθ,m·n=ax+by+cz