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Aula: Expressando um Segmento de Reta Direcionado no Espaço

Atividade • 10 Questões

Q1:

Para os pontos 𝑃 = ( 0 , 0 , 0 ) , 𝑄 = ( 1 , 3 , 2 ) , 𝑅 = ( 1 , 0 , 1 ) , e 𝑆 = ( 2 , 3 , 4 ) , seria οƒͺ 𝑃 𝑄 = οƒͺ 𝑅 𝑆 ?

  • Asim
  • BnΓ£o

Q2:

Dados pontos 𝐴 = ( βˆ’ 5 , 2 , βˆ’ 2 ) , e 𝐡 = ( βˆ’ 8 , 9 , 5 ) , encontre  𝐴 𝐡 e  𝐡 𝐴 .

  • A  𝐴 𝐡 = ( βˆ’ 3 , 7 , 7 ) ,  𝐡 𝐴 = ( 3 , βˆ’ 7 , βˆ’ 7 )
  • B  𝐴 𝐡 = ( 3 , βˆ’ 7 , βˆ’ 7 ) ,  𝐡 𝐴 = ( βˆ’ 3 , 7 , 7 )
  • C  𝐴 𝐡 = ( βˆ’ 3 , 7 , 7 ) ,  𝐡 𝐴 = ( βˆ’ 6 , 5 , 1 )
  • D  𝐴 𝐡 = ( βˆ’ 1 3 , 1 1 , 3 ) ,  𝐡 𝐴 = ( 3 , βˆ’ 7 , βˆ’ 7 )

Q3:

Dados pontos 𝐴 = ( βˆ’ 1 , 6 , βˆ’ 7 ) , e 𝐡 = ( βˆ’ 1 , βˆ’ 7 , βˆ’ 2 ) , encontre  𝐴 𝐡 e  𝐡 𝐴 .

  • A  𝐴 𝐡 = ( 0 , βˆ’ 1 3 , 5 ) ,  𝐡 𝐴 = ( 0 , 1 3 , βˆ’ 5 )
  • B  𝐴 𝐡 = ( 0 , 1 3 , βˆ’ 5 ) ,  𝐡 𝐴 = ( 0 , βˆ’ 1 3 , 5 )
  • C  𝐴 𝐡 = ( 0 , βˆ’ 1 3 , 5 ) ,  𝐡 𝐴 = ( βˆ’ 1 , 0 , βˆ’ 4 )
  • D  𝐴 𝐡 = ( βˆ’ 2 , βˆ’ 1 , βˆ’ 9 ) ,  𝐡 𝐴 = ( 0 , 1 3 , βˆ’ 5 )

Q4:

Dados pontos 𝐴 = ( 9 , 9 , 6 ) , e 𝐡 = ( 6 , 8 , βˆ’ 4 ) , encontre  𝐴 𝐡 e  𝐡 𝐴 .

  • A  𝐴 𝐡 = ( βˆ’ 3 , βˆ’ 1 , βˆ’ 1 0 ) ,  𝐡 𝐴 = ( 3 , 1 , 1 0 )
  • B  𝐴 𝐡 = ( 3 , 1 , 1 0 ) ,  𝐡 𝐴 = ( βˆ’ 3 , βˆ’ 1 , βˆ’ 1 0 )
  • C  𝐴 𝐡 = ( βˆ’ 3 , βˆ’ 1 , βˆ’ 1 0 ) ,  𝐡 𝐴 = ( 7 , 8 , 1 )
  • D  𝐴 𝐡 = ( 1 5 , 1 7 , 2 ) ,  𝐡 𝐴 = ( 3 , 1 , 1 0 )

Q5:

As coordenadas de 𝐴 e 𝐡 sΓ£o ( 1 , βˆ’ 5 , 2 ) e ( 0 , βˆ’ 4 , βˆ’ 2 ) respectivamente. Se 𝐢 Γ© o ponto mΓ©dio de 𝐴 𝐡 , qual Γ© οƒͺ 𝐡 𝐢 ?

  • A ο€Ό 1 2 , βˆ’ 1 2 , 2 
  • B ο€Ό βˆ’ 1 2 , 1 2 , βˆ’ 2 
  • C ( 1 , βˆ’ 1 , 4 )
  • D ( βˆ’ 1 , 1 , βˆ’ 4 )

Q6:

As coordenadas de 𝐴 e 𝐡 sΓ£o ( βˆ’ 4 , 4 , 5 ) e ( 4 , 0 , βˆ’ 4 ) respectivamente. Se 𝐢 Γ© o ponto mΓ©dio de 𝐴 𝐡 , qual Γ© οƒͺ 𝐡 𝐢 ?

  • A ο€Ό βˆ’ 4 , 2 , 9 2 
  • B ο€Ό 4 , βˆ’ 2 , βˆ’ 9 2 
  • C ( βˆ’ 8 , 4 , 9 )
  • D ( 8 , βˆ’ 4 , βˆ’ 9 )

Q7:

As coordenadas de 𝐴 e 𝐡 sΓ£o ( 1 , 5 , βˆ’ 2 ) e ( βˆ’ 4 , βˆ’ 2 , 0 ) respectivamente. Se 𝐢 Γ© o ponto mΓ©dio de 𝐴 𝐡 , qual Γ© οƒͺ 𝐡 𝐢 ?

  • A ο€Ό 5 2 , 7 2 , βˆ’ 1 
  • B ο€Ό βˆ’ 5 2 , βˆ’ 7 2 , 1 
  • C ( 5 , 7 , βˆ’ 2 )
  • D ( βˆ’ 5 , βˆ’ 7 , 2 )

Q8:

Dados  𝐴 𝐡 = ( βˆ’ 1 , βˆ’ 3 , 0 ) e βƒ— 𝐴 = ( βˆ’ 4 , βˆ’ 5 , βˆ’ 5 ) , expresse βƒ— 𝐡 em termos dos vetores unitΓ‘rios fundamentais.

  • A βˆ’ 5 βƒ— 𝚀 βˆ’ 8 βƒ— πš₯ βˆ’ 5 βƒ— π‘˜
  • B 3 βƒ— 𝚀 + 2 βƒ— πš₯ + 5 βƒ— π‘˜
  • C 5 βƒ— 𝚀 + 8 βƒ— πš₯ + 5 βƒ— π‘˜
  • D βˆ’ 3 βƒ— 𝚀 βˆ’ 2 βƒ— πš₯ βˆ’ 5 βƒ— π‘˜

Q9:

Dados  𝐴 𝐡 = ( 2 , 4 , 3 ) e βƒ— 𝐴 = ( βˆ’ 3 , 1 , 2 ) , expresse βƒ— 𝐡 em termos dos vetores unitΓ‘rios fundamentais.

  • A βˆ’ βƒ— 𝚀 + 5 βƒ— πš₯ + 5 βƒ— π‘˜
  • B 5 βƒ— 𝚀 + 3 βƒ— πš₯ + βƒ— π‘˜
  • C βƒ— 𝚀 βˆ’ 5 βƒ— πš₯ βˆ’ 5 βƒ— π‘˜
  • D βˆ’ 5 βƒ— 𝚀 βˆ’ 3 βƒ— πš₯ βˆ’ βƒ— π‘˜

Q10:

Dados  𝐴 𝐡 = ( 2 , βˆ’ 4 , βˆ’ 1 ) e βƒ— 𝐴 = ( 3 , 1 , 0 ) , expresse βƒ— 𝐡 em termos dos vetores unitΓ‘rios fundamentais.

  • A 5 βƒ— 𝚀 βˆ’ 3 βƒ— πš₯ βˆ’ βƒ— π‘˜
  • B βˆ’ βƒ— 𝚀 βˆ’ 5 βƒ— πš₯ βˆ’ βƒ— π‘˜
  • C βˆ’ 5 βƒ— 𝚀 + 3 βƒ— πš₯ + βƒ— π‘˜
  • D βƒ— 𝚀 + 5 βƒ— πš₯ + βƒ— π‘˜
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