Question

已知平行四边形ABCD的顶点A(-1,-2) B(3,-1)C(5,6) ①求D点坐标 ②设对角线AC,BD交于E 求c

Answer 1

①设D(x,y),则向量CD=(x-5,y-6)=BA=(-4,-1),

∴x=1,y=5,即D(1,5).

②AC=(6,8),BD=(-2,6),

AC*BD=-12+48=36,

|AC|=10,|BD|=2√10,

cosAEB=AC*BD/(|AC|*|BD|)=9√10/50,

③（AB-tOC)⊥OC,

∴0=（AB-tOC)*OC=AB*OC-tOC^=(4,1)*(5,6)-61t

=26-61t,

∴t=26/61.