(!)利用平面向量数量积证明不等式(x²+y²)(m²+n²)≥(xm...
发布网友
发布时间：2024-10-23 23:04
共2个回答
热心网友
时间：2024-11-01 13:03
平面向量u = (x,y)
平面向量v = (m,n)
数量积 u*v = |u||v|cos <u,v)>
u*v <= |u||v| => |u|^2 * |v|^2 <= (u*v)^2
==> （x²+y²)(m²+n²) ≥ (xm+yn)²
(2) u = (cos a, sin a), a = the angle between x-axis and u
v = (cos b, sin b), b = the angle between x-axis and v.
angle <u,v> is the angle between u, v. ==> <u,v> = b - a.
数量积u*v = cos a * cos b + sin a * sin b
|u| = (cos^2 a + sin^2 a)^(1/2) = 1
|v| = 1.
u*v = |u||v| cos <u,v> = cos <u,v> = cos (b-a)
So, cos(b-a) = cos a cos b + sin a sin b
热心网友
时间：2024-11-01 13:04
向量U平方是绝对值U的平方
