在长方体ABCD-A 1 B 1 C 1 D 1 中,AB=BC=2,过A 1 、C 1 、B三点的平面截去长方体的一个角后得到如图所示的几何体ABCD-A 1 C 1 D,且这个几何体的体积为 。 (1)求A 1 A的长; (2)在线段BC 1 上是否存在点P,使直线A 1 P与C 1 D垂直,如果存在,求线段A 1 P的长;如果不存在,请说明理由。
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