已知向量a=(2,-1),b=(x,-2),c=(3,y),若a//b,(a+b)垂直（b-c),M(x,y),N(y,x),则向量MN的模为?

已知向量a=(2,-1),b=(x,-2),c=(3,y),若a//b,(a+b)垂直（b-c),M(x,y),N(y,x),则向量MN的模为?
已知向量a=(2,-1),b=(x,-2),c=(3,y),若a//b,(a+b)垂直（b-c),M(x,y),N(y,x),则向量MN的模为?

已知向量a=(2,-1),b=(x,-2),c=(3,y),若a//b,(a+b)垂直（b-c),M(x,y),N(y,x),则向量MN的模为?
a//b得2/x = (-1)/(-2) ,x=4
a+b=(2+4,-1-2)=(6,-3)
b-c=(1,-2-y)
(a+b) ⊥(b-c)得到6*1 + (-3)*(-2-y) = 0 得到y=-4
于是m(4,-4),n(-4,4)
|MN| = √((4-(-4))^2+((-4)-4)^2) = 8√2