Lição de casa da aula: Vetores em Rⁿ Mathematics

Nesta atividade, nós vamos praticar a generalizar o conceito de vetores para Rⁿ e como aplicar as operações de vetores em Rⁿ.

Q1:

Encontre o vetor unitΓ‘rio de 𝐴, onde 𝐴=βŽ‘βŽ’βŽ’βŽ£βˆ’547βˆ’6⎀βŽ₯βŽ₯⎦.

  • A√1414βŽ‘βŽ’βŽ’βŽ£βˆ’547βˆ’6⎀βŽ₯βŽ₯⎦
  • B√1442βŽ‘βŽ’βŽ’βŽ£βˆ’547βˆ’6⎀βŽ₯βŽ₯⎦
  • C√1414⎑⎒⎒⎣5476⎀βŽ₯βŽ₯⎦
  • D1442⎑⎒⎒⎣5476⎀βŽ₯βŽ₯⎦
  • E1442βŽ‘βŽ’βŽ’βŽ£βˆ’547βˆ’6⎀βŽ₯βŽ₯⎦

Q2:

Se 𝐴=⎑⎒⎒⎒⎒⎣243βˆ’2βˆ’4⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦, determine |𝐴|.

  • A√7
  • B√15
  • C3
  • D49
  • E7

Q3:

Se 𝐴=βŽ‘βŽ’βŽ’βŽ’βŽ’βŽ£βˆ’51328⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦ e 𝐡=⎑⎒⎒⎒⎒⎣12βˆ’124⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦, determine π΄βˆ’2𝐡.

  • AβŽ‘βŽ’βŽ’βŽ’βŽ’βŽ£βˆ’6βˆ’1404⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦
  • BβŽ‘βŽ’βŽ’βŽ’βŽ’βŽ£βˆ’7βˆ’1420⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦
  • CβŽ‘βŽ’βŽ’βŽ’βŽ’βŽ£βˆ’3βˆ’35βˆ’20⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦
  • DβŽ‘βŽ’βŽ’βŽ’βŽ’βŽ£βˆ’7βˆ’35βˆ’20⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦
  • E⎑⎒⎒⎒⎒⎣73βˆ’520⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦

Q4:

Se 𝐴=⎑⎒⎒⎒⎒⎣23βˆ’1βˆ’54⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦, 𝐡=⎑⎒⎒⎒⎒⎣47475⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦, e 𝐢=βŽ‘βŽ’βŽ’βŽ’βŽ’βŽ£βˆ’1βˆ’38βˆ’2βˆ’7⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦, encontre o valor de |𝐴+π΅βˆ’πΆ|.

  • A√199
  • B515
  • C103
  • D√103
  • E√515

Q5:

Se 𝐴=⎑⎒⎒⎣6251⎀βŽ₯βŽ₯⎦, 𝐡=⎑⎒⎒⎣2βˆ’132⎀βŽ₯βŽ₯⎦, e 𝐢=⎑⎒⎒⎣3145⎀βŽ₯βŽ₯⎦, determine 𝐴+2π΅βˆ’2𝐢.

  • A⎑⎒⎒⎣7βˆ’270⎀βŽ₯βŽ₯⎦
  • B⎑⎒⎒⎣524βˆ’2⎀βŽ₯βŽ₯⎦
  • C⎑⎒⎒⎣4βˆ’23βˆ’5⎀βŽ₯βŽ₯⎦
  • D⎑⎒⎒⎣7270⎀βŽ₯βŽ₯⎦
  • E⎑⎒⎒⎣4235⎀βŽ₯βŽ₯⎦

Q6:

Se 𝐴=⎑⎒⎒⎣5βˆ’364⎀βŽ₯βŽ₯⎦, determine 2𝐴.

  • A⎑⎒⎒⎣106128⎀βŽ₯βŽ₯⎦
  • B⎑⎒⎒⎣106βˆ’128⎀βŽ₯βŽ₯⎦
  • C⎑⎒⎒⎣7βˆ’586⎀βŽ₯βŽ₯⎦
  • D⎑⎒⎒⎣10βˆ’6128⎀βŽ₯βŽ₯⎦
  • E⎑⎒⎒⎣7βˆ’186⎀βŽ₯βŽ₯⎦

Q7:

Se 𝐴=βŽ‘βŽ’βŽ’βŽ£βˆ’9βˆ’182⎀βŽ₯βŽ₯⎦ e 𝐡=⎑⎒⎒⎣2βˆ’383⎀βŽ₯βŽ₯⎦, determine π΅βˆ’π΄.

  • AβŽ‘βŽ’βŽ’βŽ£βˆ’11201⎀βŽ₯βŽ₯⎦
  • B⎑⎒⎒⎣11βˆ’201⎀βŽ₯βŽ₯⎦
  • C⎑⎒⎒⎣720βˆ’1⎀βŽ₯βŽ₯⎦
  • D⎑⎒⎒⎣1120βˆ’1⎀βŽ₯βŽ₯⎦
  • E⎑⎒⎒⎣7βˆ’201⎀βŽ₯βŽ₯⎦

Q8:

Se 𝐴=⎑⎒⎒⎒⎒⎣1βˆ’8745⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦ e 𝐡=⎑⎒⎒⎒⎒⎣1βˆ’153βˆ’2⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦, encontre 𝐴+𝐡.

  • A⎑⎒⎒⎒⎒⎣2βˆ’71273⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦
  • B⎑⎒⎒⎒⎒⎣271277⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦
  • C⎑⎒⎒⎒⎒⎣2βˆ’91273⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦
  • D⎑⎒⎒⎒⎒⎣2βˆ’71277⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦
  • E⎑⎒⎒⎒⎒⎣2βˆ’91277⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦

Q9:

Encontre o vetor unitΓ‘rio na mesma direção do vetor 26.

  • A⎑⎒⎒⎣√10√103⎀βŽ₯βŽ₯⎦
  • B⎑⎒⎒⎣120320⎀βŽ₯βŽ₯⎦
  • C⎑⎒⎒⎒⎣√10103√1010⎀βŽ₯βŽ₯βŽ₯⎦
  • D11
  • E⎑⎒⎒⎒⎒⎣2√86√8⎀βŽ₯βŽ₯βŽ₯βŽ₯⎦

Q10:

Calcule 5(1,2+3𝑖,3,βˆ’2)+6(2βˆ’π‘–,1,βˆ’2,7).

  • A(33βˆ’11𝑖,33+33𝑖,11,55)
  • B(13βˆ’6𝑖,8+3𝑖,βˆ’9,40)
  • C(17βˆ’6𝑖,16+15𝑖,3,32)
  • D(7βˆ’π‘–,11+15𝑖,13,βˆ’3)
  • E(3βˆ’π‘–,3+3𝑖,1,5)

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