如圖所示,正方體
ABCD-A1B1C1D1的棱長為
a,
M、
N分別為
A1B和
AC上的點,
A1M=
AN=
a,則
MN與平面
BB1C1C的位置關系是________.

分別以
C1B1、
C1D1、
C1C所在直線為
x,
y,
z軸,建立空間直角坐標系,如圖所示.

∵
A1M=
AN=
a,
∴
M
,
N
,∴

=

.
又
C1(0,0,0),
D1(0,
a,0),
∴

=(0,
a,0),∴

·

=0,∴

⊥

.
∵

是平面
BB1C1C的法向量,且
MN?平面
BB1C1C,∴
MN∥平面
BB1C1C.
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
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在
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
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