Atividade: Forma em Coordenadas de um Vetor

Nesta atividade, nós vamos praticar a expressar um vetor em forma de componente, dados seus pontos inicial e terminal.

Q1:

Determine as coordenadas de um vetor  𝐴 𝐡 , em que 𝐴 = ( βˆ’ 4 , 5 , 1 , 2 ) e 𝐡 = ( βˆ’ 4 , 5 , 5 , 7 ) .

  • A ( βˆ’ 4 , 5 , 1 , 2 )
  • B ( 4 , 5 , 0 )
  • C ( βˆ’ 4 , 5 , 5 , 7 )
  • D ( 0 , 4 , 5 )
  • E ( 0 , βˆ’ 4 , 5 )

Q2:

Determine as coordenadas do ponto terminal do vetor representado na figura.

  • A ( βˆ’ 3 , βˆ’ 2 )
  • B ( 1 , 4 )
  • C ( βˆ’ 4 , βˆ’ 1 )
  • D ( 4 , 1 )
  • E ( βˆ’ 2 , βˆ’ 3 )

Q3:

Determine as coordenadas do ponto inicial do vetor representado na figura.

  • A ( βˆ’ 3 , βˆ’ 3 )
  • B ( βˆ’ 3 , 3 )
  • C ( 3 , 3 )
  • D ( 3 , βˆ’ 3 )
  • E ( βˆ’ 2 , 1 )

Q4:

Determine as coordenadas do vetor  𝐴 𝐡 , em que 𝐴 = ( 1 , 5 , βˆ’ 0 , 3 ) e 𝐡 = ( βˆ’ 1 , 5 ) .

  • A ( 1 , 5 , βˆ’ 0 , 3 )
  • B ( 5 , 3 , βˆ’ 2 , 5 )
  • C ( βˆ’ 1 , 5 )
  • D ( βˆ’ 2 , 5 , 5 , 3 )
  • E ( 2 , 5 , βˆ’ 5 , 3 )

Q5:

Um vetor tem coordenadas ( βˆ’ 1 , βˆ’ 2 ) e tem como ponto terminal ( βˆ’ 9 , 0 ) . Qual Γ© o seu ponto inicial?

  • A ( βˆ’ 1 0 , βˆ’ 2 )
  • B ( 8 , βˆ’ 2 )
  • C ( 2 , βˆ’ 8 )
  • D ( βˆ’ 8 , 2 )
  • E ( βˆ’ 8 , βˆ’ 2 )

Q6:

O ponto inicial do vetor mostrado no diagrama Γ© a origem, ( 0 , 0 ) .

Quais sΓ£o as coordenadas do seu ponto terminal?

  • A ( 1 , 2 )
  • B ( βˆ’ 2 , βˆ’ 1 )
  • C ( 2 , 1 )
  • D ( βˆ’ 1 , βˆ’ 2 )
  • E ( 1 , βˆ’ 2 )

Quais sΓ£o as componentes do vetor?

  • A ( βˆ’ 1 , βˆ’ 2 )
  • B ( 2 , 1 )
  • C ( 1 , 2 )
  • D ( βˆ’ 2 , βˆ’ 1 )
  • E ( 1 , βˆ’ 2 )

Q7:

O ponto inicial do vetor mostrado no diagrama Γ© a origem, ( 0 , 0 ) .

Quais sΓ£o as coordenadas do seu ponto terminal?

  • A ( βˆ’ 3 , βˆ’ 1 )
  • B ( βˆ’ 1 , 3 )
  • C ( 3 , 1 )
  • D ( 3 , βˆ’ 1 )
  • E ( βˆ’ 3 , 1 )

Quais sΓ£o as componentes do vetor?

  • A ( 3 , βˆ’ 1 )
  • B ( 3 , 1 )
  • C ( βˆ’ 3 , βˆ’ 1 )
  • D ( βˆ’ 1 , 3 )
  • E ( βˆ’ 3 , 1 )

Q8:

O ponto inicial do vetor mostrado no diagrama Γ© a origem, ( 0 , 0 ) .

Quais sΓ£o as coordenadas do seu ponto terminal?

  • A ( 2 , βˆ’ 3 )
  • B ( 2 , 3 )
  • C ( βˆ’ 2 , βˆ’ 3 )
  • D ( βˆ’ 2 , 3 )
  • E ( βˆ’ 3 , 2 )

Quais sΓ£o as componentes do vetor?

  • A ( βˆ’ 2 , 3 )
  • B ( βˆ’ 2 , βˆ’ 3 )
  • C ( 2 , βˆ’ 3 )
  • D ( 2 , 3 )
  • E ( βˆ’ 3 , 2 )

Q9:

Considere o vetor representado na figura.

Quais sΓ£o as coordenadas do seu ponto terminal?

  • A ( 1 , 3 )
  • B ( βˆ’ 2 , βˆ’ 2 )
  • C ( 2 , 2 )
  • D ( 3 , 1 )
  • E ( 5 , 3 )

Quais sΓ£o as coordenadas do seu ponto inicial?

  • A ( βˆ’ 2 , βˆ’ 2 )
  • B ( 2 , 2 )
  • C ( 1 , 3 )
  • D ( 3 , 1 )
  • E ( 5 , 3 )

Quais sΓ£o as coordenadas do vetor?

  • A ( βˆ’ 5 , βˆ’ 3 )
  • B ( 3 , 5 )
  • C ( 5 , 3 )
  • D ( 3 , 1 )
  • E ( βˆ’ 2 , βˆ’ 2 )

Q10:

Considere o vetor representado na figura.

Quais sΓ£o as coordenadas do seu ponto terminal?

  • A ( 4 , 1 )
  • B ( 7 , 4 )
  • C ( 7 , 1 )
  • D ( 1 , 4 )
  • E ( βˆ’ 6 , 0 )

Quais sΓ£o as coordenadas do seu ponto inicial?

  • A ( 7 , 4 )
  • B ( 4 , 1 )
  • C ( 4 , 7 )
  • D ( 1 , 4 )
  • E ( βˆ’ 6 , 0 )

Quais sΓ£o as coordenadas do vetor?

  • A ( 6 , 0 )
  • B ( 0 , βˆ’ 6 )
  • C ( βˆ’ 6 , 0 )
  • D ( 7 , 4 )
  • E ( 1 , 4 )

Q11:

Considere o vetor representado na figura.

Quais sΓ£o as coordenadas do seu ponto terminal?

  • A ( βˆ’ 2 , βˆ’ 4 )
  • B ( βˆ’ 4 , 3 )
  • C ( 3 , βˆ’ 4 )
  • D ( βˆ’ 4 , βˆ’ 2 )
  • E ( 0 , βˆ’ 5 )

Quais sΓ£o as coordenadas do seu ponto inicial?

  • A ( βˆ’ 4 , 3 )
  • B ( 3 , βˆ’ 4 )
  • C ( βˆ’ 2 , βˆ’ 4 )
  • D ( βˆ’ 4 , βˆ’ 2 )
  • E ( 0 , βˆ’ 5 )

Quais sΓ£o as coordenadas do vetor?

  • A ( 0 , 5 )
  • B ( βˆ’ 5 , 0 )
  • C ( 0 , βˆ’ 5 )
  • D ( βˆ’ 4 , 3 )
  • E ( βˆ’ 4 , βˆ’ 2 )

Q12:

Considere o vetor representado na figura.

Quais sΓ£o as coordenadas do seu ponto terminal?

  • A ( 2 , 1 )
  • B ( 1 , 4 )
  • C ( 4 , 1 )
  • D ( 1 , 2 )
  • E ( 0 , βˆ’ 2 )

Quais sΓ£o as coordenadas do seu ponto inicial?

  • A ( 1 , 4 )
  • B ( 2 , 1 )
  • C ( 4 , 1 )
  • D ( 1 , 2 )
  • E ( 0 , βˆ’ 2 )

Quais sΓ£o as coordenadas do vetor?

  • A ( 0 , 2 )
  • B ( βˆ’ 2 , 0 )
  • C ( 0 , βˆ’ 2 )
  • D ( 1 , 2 )
  • E ( 1 , 4 )

Q13:

Considere o vetor representado na figura.

Quais sΓ£o as coordenadas do seu ponto terminal?

  • A ( 1 , 2 )
  • B ( 3 , 4 )
  • C ( 4 , 3 )
  • D ( 2 , 1 )
  • E ( βˆ’ 1 , βˆ’ 3 )

Quais sΓ£o as coordenadas do seu ponto inicial?

  • A ( 3 , 4 )
  • B ( 4 , 3 )
  • C ( 1 , 2 )
  • D ( 2 , 1 )
  • E ( βˆ’ 1 , βˆ’ 3 )

Quais sΓ£o as coordenadas do vetor?

  • A ( 1 , 3 )
  • B ( βˆ’ 3 , βˆ’ 1 )
  • C ( βˆ’ 1 , βˆ’ 3 )
  • D ( 2 , 1 )
  • E ( 3 , 4 )

Q14:

Suponha que as coordenadas dos pontos 𝐴 e 𝐡 sΓ£o ( π‘₯ , 𝑦 )   e ( π‘₯ , 𝑦 )   respectivamente. Encontre os componentes do vetor  𝐴 𝐡 em termos de π‘₯  , 𝑦  , π‘₯  , e 𝑦  .

  • A ( 𝑦 βˆ’ 𝑦 , π‘₯ βˆ’ π‘₯ )    
  • B ( π‘₯ + π‘₯ , 𝑦 + 𝑦 )    
  • C ( 𝑦 + 𝑦 , π‘₯ + π‘₯ )    
  • D ( π‘₯ βˆ’ π‘₯ , 𝑦 βˆ’ 𝑦 )    
  • E ( π‘₯ βˆ’ π‘₯ , 𝑦 βˆ’ 𝑦 )    

Q15:

Um vetor tem coordenadas ( βˆ’ 3 , 5 ) e tem ponto inicial ( 2 , βˆ’ 5 ) . Qual Γ© o seu ponto terminal?

  • A ( βˆ’ 5 , 1 0 )
  • B ( 5 , βˆ’ 1 0 )
  • C ( 0 , βˆ’ 1 )
  • D ( βˆ’ 1 , 0 )
  • E ( 1 , 0 )

Q16:

Determine as coordenadas do vetor  𝐴 𝐡 , em que 𝐴 = ( 1 5 , 3 , βˆ’ 5 ) e 𝐡 = ( βˆ’ 3 , 7 , βˆ’ 5 ) .

  • A ( 1 5 , 3 , βˆ’ 5 )
  • B ( 0 , βˆ’ 1 9 )
  • C ( βˆ’ 3 , 7 , βˆ’ 5 )
  • D ( βˆ’ 1 9 , 0 )
  • E ( 1 9 , 0 )

Q17:

Determine as coordenadas do vetor  𝐴 𝐡 .

  • A ( 4 , βˆ’ 1 , 7 )
  • B ( 1 , 9 , βˆ’ 3 )
  • C ( 4 , 1 , 9 )
  • D ( βˆ’ 3 , 1 , 9 )
  • E ( βˆ’ 3 , βˆ’ 1 , 7 )

Q18:

Dado que as coordenadas de 𝐴 e 𝐡 sΓ£o ( βˆ’ 1 2 , βˆ’ 2 4 ) e ( βˆ’ 3 , 1 6 ) respectivamente, encontre | |  𝐴 𝐡 | | .

Q19:

Determine as coordenadas de um vetor  𝐴 𝐡 , em que 𝐴 = ( βˆ’ 1 9 , βˆ’ 4 , 1 ) e 𝐡 = ( βˆ’ 4 , 4 , βˆ’ 9 , 7 ) .

  • A ( βˆ’ 1 9 , βˆ’ 4 , 1 )
  • B ( βˆ’ 5 , 6 , 1 4 , 6 )
  • C ( βˆ’ 4 , 4 , βˆ’ 9 , 7 )
  • D ( 1 4 , 6 , βˆ’ 5 , 6 )
  • E ( βˆ’ 1 4 , 6 , 5 , 6 )

Q20:

Utilizando o grΓ‘fico mostrado, determine o vetor de posição do ponto 𝐢 em relação ao ponto de origem 𝑂 , denotado por  𝑂 𝐢 , e encontre sua norma, denotada por | |  𝑂 𝐢 | | .

  • A  𝑂 𝐢 = ( 9 , 6 ) , | |  𝑂 𝐢 | | = 3 √ 1 3
  • B  𝑂 𝐢 = ( βˆ’ 9 , βˆ’ 6 ) , | |  𝑂 𝐢 | | = √ 1 5
  • C  𝑂 𝐢 = ( βˆ’ 6 , βˆ’ 9 ) , | |  𝑂 𝐢 | | = 3 √ 1 3
  • D  𝑂 𝐢 = ( βˆ’ 9 , βˆ’ 6 ) , | |  𝑂 𝐢 | | = 3 √ 1 3
  • E  𝑂 𝐢 = ( βˆ’ 6 , βˆ’ 9 ) , | |  𝑂 𝐢 | | = √ 1 5

Q21:

Os pontos 𝐴 , 𝐡 , e 𝐢 tem coordenadas ( βˆ’ 7 , 1 ) , ( βˆ’ 2 , 4 ) , e ( βˆ’ 4 , βˆ’ 1 ) respectivamente. Dado que  𝐴 𝐡 e  𝐢 𝐷 sΓ£o vetores equivalentes, encontre as coordenadas de 𝐷 .

  • A ( 9 , 4 )
  • B ( 2 , 1 )
  • C ( 4 , 9 )
  • D ( 1 , 2 )
  • E ( βˆ’ 9 , βˆ’ 4 )

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