Texte intégral
6.12 1) ~a+~b−~c= (2e~1−e~2 + 5e~3) + (e~1−e~3)−(e~1+e~2−3e~3)
= 2e~1−e~2+ 5e~3+e~1−e~3 −e~1 −e~2+ 3e~3
= 2e~1−2e~2+ 7e~3
2) 3~a+ 3~b= 3 (2e~1−e~2 + 5e~3) + 3 (e~1−e~3)
= 6e~1−3e~2+ 15e~3+ 3e~1−3e~3
= 9e~1−3e~2+ 12e~3
3) ~a−~b−~c= (2e~1−e~2+ 5e~3)−(e~1−e~3)−(e~1+e~2−3e~3)
= 2e~1−e~2+ 5e~3−e~1+e~3−e~1−e~2+ 3e~3
=−2e~2+ 9e~3
4) 3~a+ 2~c= 3 (2e~1−e~2 + 5e~3) + 2 (e~1+e~2−3e~3)
= 6e~1−3e~2+ 15e~3+ 2e~1+ 2e~2−6e~3
= 8e~1−e~2+ 9e~3
Géométrie : vecteurs Corrigé 6.12
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