解:(Ⅰ)证明:以A为原点,射线AB,AC,AP分别为x,y,z轴正向建立空间直角坐标系如图.
则P(0,0,1),C(0,1,0),B(2,0,0),
M(1,0,
),N(1 2
,0,0),S(1,1 2
,0),1 2
=(1,?1,CM
),1 2
=(?SN
,?1 2
,0),1 2
∵
?CM
=(1,?1,SN
)?(?1 2
,?1 2
,0)=0,1 2
∴CM⊥SN.
(Ⅱ)设
=(0,0,1)为平面CBA的法向量,m
=(2,?1,0),CB
PC