(1)将a=(1,-2);b=(-3,1);c=(11,-7)代入c=xa+yb得(11,-7)=(x,-2x)+(-3y,y)即x-3y=11,-2x+y=-7解方程组,得x=2,y=-3(2)设D(x,y) 向量AB=(1,-2),向量BC=(-6,1),向量AC=(-5,-1),CD=(x+3,y),BD=(x-3,y+1)分两种情况:当AB平行CD时,AB=CD或者AB=-CD解得x=-2,y=-2或者x=-4,y=2所以此时D坐标为(-2,-2)或者(-4,2)当AC平行BD时候,有AC=BD或者AC=-BD解得x=-2,y=-2或者x=8,y=0所以此时D的坐标为(-2,-2)或者(8,0) |