已知空间四边形OABC,其对角线为OB,AC,M,N分别是对边OA,BC的中点,点G在线段MN上,且MG=2GN,现用基组{OA,OB,OC}表示向量OG,有OG=xOA+yOB+zOC,则x,y,z

题目简介

已知空间四边形OABC,其对角线为OB,AC,M,N分别是对边OA,BC的中点,点G在线段MN上,且MG=2GN,现用基组{OA,OB,OC}表示向量OG,有OG=xOA+yOB+zOC,则x,y,z

题目详情

已知空间四边形OABC,其对角线为OB,AC,M,N分别是对边OA,BC的中点,点G在线段MN上,且
MG
=2
GN
,现用基组{
OA
OB
OC
}表示向量
OG
,有
OG
=x
OA
+y
OB
+z
OC
,则x,y,z的值分别为______.
题型:填空题难度:中档来源:不详

答案

如图所示,
OG
=
OM
+
MG
OM
=class="stub"1
2
OA
MG
=class="stub"2
3
MN
MN
=
ON
-
OM
ON
=class="stub"1
2
(
OB
+
OC
)

OG
=class="stub"1
2
OA
+class="stub"2
3
[class="stub"1
2
(
OB
+
OC
)-class="stub"1
2
OA
]

=class="stub"5
6
OA
+class="stub"1
3
OB
+class="stub"1
3
OC

又有
OG
=x
OA
+y
OB
+z
OC

x=class="stub"5
6
y=z=class="stub"1
3

故答案为:class="stub"5
6
class="stub"1
3
class="stub"1
3

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