在梯形ABCD中,BC//AD,AC垂直BD,AB向量=(6,1),BC向量=(X,Y),CD向量=(-2,-3) 求X

向量AD=AB+BC+CD=(4+x,y-2),向量BC =(X,Y),
又因BC//AD,所以(4+x)y- (y-2)x=0.即x=-2y……①
向量AC=AB+BC=(x+6,y+1),向量BD=BC+CD=(x-2,y-3),
又因AC⊥BD,所以(x+6)(x-2)+(y+1) (y-3)=0.……②
联立①②解得：x=2,y=-1或x=-6,y=3.