October 2023 1 51 Report
Escolha a opção que possui o determinante da matriz A equals open square brackets table row 0 1 2 0 1 row 0 0 0 0 0 row 1 2 5 7 1 row 1 1 0 2 1 row 1 0 1 1 1 end table close square brackets a. det(A) = π b. det(A) = 2 c. det(A) = 0 d. det(A) = -1 e. det(A) = 1
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Assinale a opção que apresenta a equação paramétrica da reta que tem a mesma direção do vetor v with rightwards arrow on top equals open parentheses negative 1 comma 2 comma 0 close parentheses e que passa pelo ponto P equals open parentheses 0 comma 1 comma 5 close parentheses. a. open curly brackets table attributes columnalign left end attributes row cell x equals negative t end cell row cell y equals 2 plus 2 t end cell row cell z equals 5 end cell end table close b. open curly brackets table attributes columnalign left end attributes row cell x equals negative t end cell row cell y equals 1 plus 2 t end cell row cell z equals 5 end cell end table close c. open curly brackets table attributes columnalign left end attributes row cell x equals 1 minus t end cell row cell y equals 1 plus 2 t end cell row cell z equals 5 end cell end table close d. open curly brackets table attributes columnalign left end attributes row cell x equals negative 2 t end cell row cell y equals 1 plus 2 t end cell row cell z equals 5 end cell end table close e. open curly brackets table attributes columnalign left end attributes row cell x equals negative t end cell row cell y equals 1 plus 2 t end cell row cell z equals 5 plus t end cell end table close
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Assinale a alternativa que apresenta as equações paramétricas da reta que passa pelos pontos P subscript 1 equals open parentheses 1 comma space 2 comma negative 1 close parentheses space e space P subscript 2 equals left parenthesis negative 2 comma space 0 comma negative 1 right parenthesis . a. open curly brackets table attributes columnalign left end attributes row cell x equals space 1 minus 3 t end cell row cell y equals space 3 minus 2 t end cell row cell z equals negative 1 end cell end table close b. open curly brackets table attributes columnalign left end attributes row cell x equals space 2 minus 3 t end cell row cell y equals space 2 minus 2 t end cell row cell z equals negative 1 end cell end table close c. open curly brackets table attributes columnalign left end attributes row cell x equals space 1 minus 3 t end cell row cell y equals space 2 minus 2 t end cell row cell z equals negative 1 end cell end table close d. open curly brackets table attributes columnalign left end attributes row cell x equals space 1 minus 2 t end cell row cell y equals space 2 end cell row cell z equals negative 1 minus t end cell end table close e. open curly brackets table attributes columnalign left end attributes row cell x equals space 1 minus 3 t end cell row cell y equals space 2 minus 2 t end cell row cell z equals negative 2 end cell end table close
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Assinale a opção que apresenta a equação paramétrica do plano definido pelos vetores u with rightwards arrow on top equals left parenthesis 1 comma 1 comma 2 right parenthesis space e space v with rightwards arrow on top equals left parenthesis negative 1 comma 1 comma 3 right parenthesis comma e que passa pelo ponto P equals left parenthesis 0 comma 3 comma negative 2 right parenthesis a. open curly brackets table attributes columnalign left end attributes row cell x equals t minus 2 h end cell row cell y equals 3 plus t plus h end cell row cell z equals negative 2 plus 2 t plus 3 h end cell end table close b. open curly brackets table attributes columnalign left end attributes row cell x equals t minus h end cell row cell y equals 3 plus t plus h end cell row cell z equals negative 3 plus 2 t plus 3 h end cell end table close c. open curly brackets table attributes columnalign left end attributes row cell x equals t minus h end cell row cell y equals 4 plus t plus h end cell row cell z equals negative 2 plus 2 t plus 3 h end cell end table close d. open curly brackets table attributes columnalign left end attributes row cell x equals t minus h end cell row cell y equals 3 plus t plus h end cell row cell z equals negative 2 plus 2 t plus 3 h end cell end table close e. open curly brackets table attributes columnalign left end attributes row cell x equals 1 plus t minus h end cell row cell y equals 3 plus t plus h end cell row cell z equals negative 2 plus 2 t plus 3 h end cell end table close
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Assinale a opção que apresenta a distância correta entre os planos straight pi subscript 1 colon space straight x plus straight y minus straight z plus 2 equals 0 space straight e space straight pi subscript 2 colon space straight x plus 2 straight y minus straight z minus 1 equals 0 a. d open parentheses straight pi subscript 1 comma straight pi subscript 2 close parentheses equals 1 b. d open parentheses straight pi subscript 1 comma straight pi subscript 2 close parentheses equals square root of 2 c. d open parentheses straight pi subscript 1 comma straight pi subscript 2 close parentheses equals 0 d. d open parentheses straight pi subscript 1 comma straight pi subscript 2 close parentheses equals fraction numerator square root of 2 over denominator 2 end fraction e. d open parentheses straight pi subscript 1 comma straight pi subscript 2 close parentheses equals square root of 6
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Assinale a alternativa que apresenta a distância correta entre os planos straight pi subscript 1 colon 2 straight x plus straight y minus straight z plus 2 equals 0 space straight e space straight pi subscript 2 colon space 4 straight x plus 2 straight y minus 2 straight z minus 5 equals 0. a. d open parentheses straight pi subscript 1 comma straight pi subscript 2 close parentheses equals 0 b. d open parentheses straight pi subscript 1 comma straight pi subscript 2 close parentheses equals 5 c. d open parentheses straight pi subscript 1 comma straight pi subscript 2 close parentheses equals 1 d. d open parentheses straight pi subscript 1 comma straight pi subscript 2 close parentheses equals fraction numerator 3 square root of 6 over denominator 4 end fraction e. d open parentheses straight pi subscript 1 comma straight pi subscript 2 close parentheses equals square root of 6
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Assinale a opção que apresenta a distância entre o ponto P equals open parentheses 1 comma negative 2 comma 1 close parentheses e o plano straight pi colon straight x plus 2 straight y minus straight z plus 3 equals 0 a. d open parentheses P comma straight pi close parentheses equals square root of 6 b. d open parentheses P comma straight pi close parentheses equals fraction numerator square root of 2 over denominator 2 end fraction c. d open parentheses P comma straight pi close parentheses equals 3 d. d open parentheses P comma straight pi close parentheses equals fraction numerator square root of 3 over denominator 3 end fraction e. d open parentheses P comma straight pi close parentheses equals fraction numerator square root of 6 over denominator 6 end fraction
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Assinale a opção que apresenta a distância entre o ponto P equals open parentheses 4 comma 1 comma 2 close parentheses e a reta r open curly brackets table attributes columnalign left end attributes row cell x equals 3 minus 2 t end cell row cell y equals 2 minus t end cell row cell z equals negative 1 plus 2 t end cell end table close a. d open parentheses P comma r close parentheses equals square root of 6 b. d open parentheses P comma r close parentheses equals square root of 8 c. d open parentheses P comma r close parentheses equals square root of 74 d. d open parentheses P comma r close parentheses equals 74 over 3 e. d open parentheses P comma r close parentheses equals fraction numerator square root of 74 over denominator 3 end fraction
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Assinale a opção que apresenta a equação normal do plano (Também chamada de equação analítica do plano) que tem vetor normal v with rightwards arrow on top equals open parentheses 1 comma 2 comma negative 3 close parentheses e que passa pelo ponto P equals open parentheses 0 comma negative 1 comma 7 close parentheses. a. x plus 2 y minus 3 z plus 23 equals 0 b. x plus 2 y plus 3 z plus 23 equals 0 c. x minus 2 y minus 3 z plus 23 equals 0 d. x plus 2 y minus 3 z minus 23 equals 0 e. x plus 2 y minus 3 z equals 0
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Sejam A equals open square brackets table row 1 0 row 1 3 end table close square brackets space e space B equals open square brackets table row 1 0 2 row 1 3 0 end table close square brackets. Escolha a opção que apresenta o resultado de AB. a. A B equals 8 b. A B equals open square brackets table row 1 0 0 row 4 9 0 end table close square brackets c. A multiplicação AB não pode ser realizada. d. A B equals open square brackets table row 1 0 row 4 9 row 2 2 end table close square brackets e. A B equals open square brackets table row 1 0 2 row 4 9 2 end table close square brackets.Alternativas B e C estão erradas...
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Escolha a opção que tem o determinante da matriz A equals open square brackets table row 0 1 0 row 1 1 2 row 1 0 1 end table close square brackets a. det(A) = -1 b. det(A) = 1 c. det(A) = π d. det(A) = 0 e. det(A) = 2
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