aula05 retas
TRANSCRIPT
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Aula 05
Retas
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Equação Vetorial
xy
z
A
B
O
X
r
AX AB����������������������������
OX OA AX ������������������������������������������
ABOAOX R
),,( 111 zyxA
),,( 222 zyxB
),,(.),,(),,( 121212111 zzyyxxzyxzyx A
- Vetor Diretorv
),,(.),,(),,( 000 cbazyxzyx R
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Equação Vetorial
P
v
r
),,( 000 zyxP
( , , )v a b c
),,(.),,(),,( 000 cbazyxzyx R
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Exemplo
Determine a equação vetorial da reta que passa pelos pontos e .
r)4,3,2(A )7,5,1( B
)4,3,2(A )7,5,1( B
( 3,2,3 )v AB ��������������
( , , ) ( 2,3,4 ) .( 3,2,3 )x y z
.
),,(.),,(),,( 000 cbazyxzyx R
R
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Exemplo
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Equações Paramétrica e Simétrica
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Exemplo
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Exemplo
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Obrigado!
Aula disponível emwww.mat.ufam.edu.br/Disney