在正方体ABCD-A1B1C1D1中,点E在A1C1上,|A1E|=14|A1C1|且AE=xAA1+yAB+zAD,则x+y+z=______.-数学

题目简介

在正方体ABCD-A1B1C1D1中,点E在A1C1上,|A1E|=14|A1C1|且AE=xAA1+yAB+zAD,则x+y+z=______.-数学

题目详情

在正方体ABCD-A1B1C1D1中,点E在A1C1上,|A1E|=
1
4
|A1C1|且
AE
=x
AA1
+y
AB
+z
AD
,则x+y+z=______.
题型:填空题难度:中档来源:不详

答案


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AB
=
A1B1
AD
A1D1

AB
+
AD
=
A1B1
+
A D1
=
A1C1

AE
AA1
 +
A1E

∵|A1E|=class="stub"1
4
|A1C1|
AE
=
AA1
+class="stub"1
4
A1C1
=
AA1
+class="stub"1
4
AB
+class="stub"1
4
AD
,,
AE
=x
AA1
+y
AB
+z
AD

∴x=1,y=class="stub"1
4
,z=class="stub"1
4

x+y+z=class="stub"3
2

故答案为class="stub"3
2

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