∴点P的坐标是P(0,0,1)或P(0,0,-1).∴|PA|=√(1^2+1^2+0)=√2或|PA|=√(1^2+1^2+2^2 )=√6.

答案√2 或√6

9.已知平行四边形ABCD,且A(4,1,3),B(2,-5,1),C(3,7,-5),则顶点D的坐标为　　　　　　　　.

解析由平行四边形对角线互相平分知,AC的中点即为BD的中点,AC的中点M(7/2 "," 4",-" 1).

　　设D(x,y,z),则7/2=(x+2)/2,4=("-" 5+y)/2,-1=(1+z)/2,∴x=5,y=13,z=-3,∴D(5,13,-3).

答案(5,13,-3)

10.

如图所示,在空间直角坐标系中,有一棱长为a的正方体ABCO-A'B'C'D',A'C的中点E到AB的中点F的距离为　　　　　.

解析由图易知A(a,0,0),B(a,a,0),C(0,a,0),A'(a,0,a).

　　∴F(a"," a/2 "," 0),E(a/2 "," a/2 "," a/2).

　　∴|EF|=√((a"-" a/2)^2+(a/2 "-" a/2)^2+(0"-" a/2)^2 )

　　=√(a^2/4+a^2/4)=√2/2a.

答案√2/2a

11.在长方体ABCD-A1B1C1D1中,|AB|=|AD|=3,|AA1|=2,点M在A1C1上,|MC1|=2|A1M|,点N在D1C上,且为D1C的中点,求M,N两点间的距离.

解分别以AB,AD,AA1所在的直线为x轴、y轴、z轴建立空间直角坐标系,如图.