Question

)利用平面向量数量积证明不等式（x²+y²)(m²+n²)≥(xm+yn)

Answer 1

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|^2 * |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 is the angle between 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 = cos = cos (b-a)

So,cos(b-a) = cos a cos b + sin a sin