9.3 1) (a)
D
A
B C H
E
F G
T M
R
−−−−→
AB = −AB−−−→
=1·
−−−−→
AB+0·
−−−−→
AD+0·
−−−−→
AE
=
1 0 0
(b)
D
A
B C H
E
F G
T M
R
−−−−→
AE =−AE−−−→
=0·
−−−−→
AB+0·
−−−−→
AD+1·
−−−−→
AE
=
0 0 1
(c)
D
A
B C H
E
F G
T M
R
−−−−→
AR =−AB−−−→+−BR−−−→
=1·
−−−−→
AB+ 1
2 ·
−−−−→
AD+0·
−−−−→
AE
=
1
1
02
(d)
D
A
B C H
E
F G
I T
M
R
−−−−→
DT =−DA−−−→+−AI−→+−IT−→
= 1
2 ·
−−−−→
AB−1·
−−−−→
AD+1
2 ·
−−−−→
AE
=
1 2
−1
1 2
(e)
D
A
B C H
E
F G
T M
R
−−−−−→
MD = −MC−−−−→+−CD−−−→
=−1·
−−−−→
AB+0·
−−−−→
AD−12 ·
−−−−→
AE
=
−1 0
−12
Géométrie : bases Corrigé 9.3
2) (a)
D
A
B C H
E
F G
T M
R
−−−−→
AB = −DC−−−→
=0·
−−−−−→
CM−1·
−−−−→
CD+0·
−−−−→
BR
=
0
−1 0
(b)
D
A
B C H
E
F G
T M
R
−−−−→
AE =−CG−−−→
=2·
−−−−−→
CM+0·
−−−−→
CD+0·
−−−−→
BR
=
2 0 0
(c)
D
A
B C H
E
F G
T M
R
−−−−→
AR =−AB−−−→+−BR−−−→
=0·
−−−−−→
CM−1·
−−−−→
CD+1·
−−−−→
BR
=
0
−1 1
(d)
D
A
B C H
E
F G
I T
M
R
−−−−→
DT =−DA−−−→+−AI−→+−IT−→
=1·
−−−−−→
CM−12 ·
−−−−→
CD+ −2·
−−−−→
BR
=
1
−12
−2
(e)
D
A
B C H
E
F G
T M
R
−−−−−→
MD = −MC−−−−→+−CD−−−→
=−1·
−−−−−→
CM+1·
−−−−→
CD+0·
−−−−→
BR
=
−1 1 0
Géométrie : bases Corrigé 9.3
