9.2 1) (a)
O A
B C
D
E F
−−−−→
EA =−EO−−−→+−OA−−−→
=1·
−−−−→
OA+1·
−−−−→
OB
=
1
1
(b)
O A
B C
D
E F
−−−−→
DC=−OB−−−→
=0·
−−−−→
OA+1·
−−−−→
OB
=
0
1
(c)
O A
B C
D
E F
−−−−→
BC =−
−−−−→
OA
=−1·
−−−−→
OA+0·
−−−−→
OB
=
−1 0
(d)
O A
B C
D
E F
−−−−→
ED =−EO−−−→+−OD−−−−→
=−1·
−−−−→
OA+1·
−−−−→
OB
=
−1 1
(e)
O A
B C
D
E F
−−−−→
CF =
−−−−→
CB+
−−−−→
BO+
−−−−→
OA+
−−−−→
AF
=2·
−−−−→
OA−2·
−−−−→
OB
=
2
−2
(f)
O A
B C
D
E F
−−−−→
AD=−AO−−−→+−OD−−−−→
=−2·
−−−−→
OA+0·
−−−−→
OB
=
−2 0
Géométrie : bases Corrigé 9.2
2) (a)
O A
B C
D
E F
−−−−→
EA =−ED−−−→+−DO−−−−→+−OA−−−→
=1·
−−−−→
OC+2·
−−−−→
OA
=
1
2
(b)
O A
B C
D
E F
−−−−→
DC=−DO−−−−→+−OC−−−→
=1·
−−−−→
OC+1·
−−−−→
OA
=
1
1
(c)
O A
B C
D
E F
−−−−→
BC =−
−−−−→
OA
=0·
−−−−→
OC−1·
−−−−→
OA
=
0
−1
(d)
O A
B C
D
E F
−−−−→
ED =−OC−−−→
=1·
−−−−→
OC+0·
−−−−→
OA
=
1
0
(e)
O A
B C
D
E F
−−−−→
CF =−CO−−−→+−OF−−−→
=−2·
−−−−→
OC+0·
−−−−→
OA
=
−2 0
(f)
O A
B C
D
E F
−−−−→
AD=−AO−−−→+−OD−−−−→
=0·
−−−−→
OC−2·
−−−−→
OA
=
0
−2
Géométrie : bases Corrigé 9.2
