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Diketahui a ⇀ = 3 i − j + 2 k dan b ⇀ = i + 2 j − 2 k . Vektor yang tegak lurus terhadap kedua vektor tersebut adalah ....

Diketahui  dan . Vektor yang tegak lurus terhadap kedua vektor tersebut adalah ....

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M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

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Jawaban

vektor yang tegak lurus terhadap kedua vektor tersebut adalah .

vektor yang tegak lurus terhadap kedua vektor tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a with rightwards harpoon with barb upwards on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell b with rightwards harpoon with barb upwards on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank i end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank j end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 7 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank k end table.

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Pembahasan

Diketahui: dan Sehingga, Vektor yang tegak lurus dengan vektor dan vektor merupakan vektor hasil dari perkalian silang . Jadi, vektor yang tegak lurus terhadap kedua vektor tersebut adalah .

Diketahui: a with rightwards harpoon with barb upwards on top equals 3 i minus j plus 2 k dan b with rightwards harpoon with barb upwards on top equals i plus 2 j minus 2 k

Sehingga, 

  • a with rightwards harpoon with barb upwards on top subscript x equals 3 comma space a with rightwards harpoon with barb upwards on top subscript y equals negative 1 comma space a with rightwards harpoon with barb upwards on top subscript z equals 2 
  • b with rightwards harpoon with barb upwards on top subscript x equals 1 comma space b with rightwards harpoon with barb upwards on top subscript y equals 2 comma space b with rightwards harpoon with barb upwards on top subscript z equals negative 2 

Vektor yang tegak lurus dengan vektor a with rightwards harpoon with barb upwards on top dan vektor b with rightwards harpoon with barb upwards on top merupakan vektor hasil dari perkalian silang a with rightwards harpoon with barb upwards on top cross times b with rightwards harpoon with barb upwards on top.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards harpoon with barb upwards on top cross times b with rightwards harpoon with barb upwards on top end cell equals cell open parentheses a with rightwards harpoon with barb upwards on top subscript y b with rightwards harpoon with barb upwards on top subscript z minus a with rightwards harpoon with barb upwards on top subscript z b with rightwards harpoon with barb upwards on top subscript y close parentheses i plus open parentheses a with rightwards harpoon with barb upwards on top subscript z b with rightwards harpoon with barb upwards on top subscript x minus a with rightwards harpoon with barb upwards on top subscript x b with rightwards harpoon with barb upwards on top subscript z close parentheses j end cell row blank blank cell plus open parentheses a with rightwards harpoon with barb upwards on top subscript x b with rightwards harpoon with barb upwards on top subscript y minus a with rightwards harpoon with barb upwards on top subscript y b with rightwards harpoon with barb upwards on top subscript x close parentheses k end cell row blank equals cell open parentheses open parentheses negative 1 close parentheses times open parentheses negative 2 close parentheses minus 2 times 2 close parentheses i plus open parentheses 2 times 1 minus 3 times open parentheses negative 2 close parentheses close parentheses j end cell row blank blank cell plus open parentheses 3 times 2 minus open parentheses negative 1 close parentheses times 1 close parentheses k end cell row blank equals cell open parentheses 2 minus 4 close parentheses i plus open parentheses 2 plus 6 close parentheses j plus open parentheses 6 plus 1 close parentheses k end cell row blank equals cell negative 2 i minus 8 j plus 7 k end cell end table     

Jadi, vektor yang tegak lurus terhadap kedua vektor tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a with rightwards harpoon with barb upwards on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell b with rightwards harpoon with barb upwards on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank i end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank j end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 7 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank k end table.

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