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(本小题满分10分)
在平面直角坐标系xOy中,点A(-1,-2)、B(2,3)、C(-2,-1).
(1)求以线段AB、AC为邻边的平行四边形两条对角线的长;
(2)设实数t满足(=0,求t的值.
(1);(2).解析:
(1)先求出,然后可以求出平行四边形的对角线对应的向量的模分别为,
(2)先求出的坐标,然后利用(=0,建立关于t的方程,从而求得t的值.
解:(1)方法一:由题设知,则
……2分
所以
故所求的两条对角线的长分别为……5分
(2)由题设知:=(-2,-1),.……7分
由(=0,得:
从而所以……10分
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