设点P在x轴上,它到P1(0,2,3)的距离为到点P2(0,1,-1)距离的两倍,则点P的坐标为(  ) A.(0,1,0)或(0,0,1) B.(0,-1,0)或(0,0,-1) C.(1,0,0)或(-1,0,0) D.(0,-

问题描述:

设点P在x轴上,它到P1(0,

2
,3)的距离为到点P2(0,1,-1)距离的两倍,则点P的坐标为(  )
A. (0,1,0)或(0,0,1)
B. (0,-1,0)或(0,0,-1)
C. (1,0,0)或(-1,0,0)
D. (0,-1,0)或(0,0,1)

设点P(a,0,0),
由题意得P1P=2P2P,即

a2+
2
2
+32
=2
a2+2

解得a=1或a=-1,
故选C.