(1)建立如图所示的空间直角坐标系,则D(0,0,0),P(0,0,1),A(1,0,0),C(0,1,0),
E,F.
设DH⊥平面PEF,垂足为H,则
\s\up6(→(→)=x\s\up6(→(→)+y\s\up6(→(→)+z\s\up6(→(→)
=,(x+y+z=1)
\s\up6(→(→)=,\s\up6(→(→)=.
所以\s\up6(→(→)·\s\up6(→(→)=x+y+-z=x+y-z=0.
同理,\s\up6(→(→)·\s\up6(→(→)=x+y-z=0,
又x+y+z=1,
所以可解得x=y=,z=.
所以\s\up6(→(→)=(2,2,3).
所以|\s\up6(→(→)|=.
因此,点D到平面PEF的距离为.
(2)连接AC,设AH′⊥平面PEF,垂足为H′,则\s\up6(→(→)∥\s\up6(→(→),设\s\up6(→(→)=λ(2,2,3)=(2λ,2λ,3λ)(λ>0),则
\s\up6(→(→)=\s\up6(→(→)+\s\up6(→(→)=+(2λ,2λ,3λ)
=.
所以\s\up6(→(→)·\s\up6(→(→)=4λ2+4λ2-λ+9λ2=0,即λ=.