Diketahui a⇀=xi+4j, b⇀=2j+2yk, dan c⇀=−5j. Jika 3(a⇀−2b⇀+c⇀)=−9i−15j+6k maka nilai x−y= ....

Pertanyaan

Diketahui begin mathsize 14px style a with rightwards harpoon with barb upwards on top equals x i plus 4 j comma space b with rightwards harpoon with barb upwards on top equals 2 j plus 2 y k comma space dan space c with rightwards harpoon with barb upwards on top equals negative 5 j end style. Jika begin mathsize 14px style 3 open parentheses a with rightwards harpoon with barb upwards on top minus 2 b with rightwards harpoon with barb upwards on top plus c with rightwards harpoon with barb upwards on top close parentheses equals negative 9 i minus 15 j plus 6 k end style maka nilai begin mathsize 14px style x minus y equals end style ....

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L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

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begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell 3 open parentheses a with rightwards harpoon with barb upwards on top minus 2 b with rightwards harpoon with barb upwards on top plus c with rightwards harpoon with barb upwards on top close parentheses end cell equals cell negative 9 i minus 15 j plus 6 k end cell row cell 3 open parentheses open parentheses table row x row 4 row 0 end table close parentheses minus 2 open parentheses table row 0 row 2 row cell 2 y end cell end table close parentheses plus open parentheses table row 0 row cell negative 5 end cell row 0 end table close parentheses close parentheses end cell equals cell open parentheses table row cell negative 9 end cell row cell negative 15 end cell row 6 end table close parentheses end cell row cell 3 open parentheses open parentheses table row x row cell 4 minus 4 minus 5 end cell row cell negative 4 y end cell end table close parentheses close parentheses end cell equals cell open parentheses table row cell negative 9 end cell row cell negative 15 end cell row 6 end table close parentheses end cell row cell open parentheses table row cell 3 x end cell row cell negative 15 end cell row cell negative 12 y end cell end table close parentheses end cell equals cell open parentheses table row cell negative 9 end cell row cell negative 15 end cell row 6 end table close parentheses end cell end table end style

dari kesamaan tersebut, diperoleh dua persamaan
begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell 3 x end cell equals cell negative 9 end cell row x equals cell negative 3 end cell row cell negative 12 y end cell equals 6 row y equals cell negative 1 half end cell end table end style

Dengan demikian, nilai begin mathsize 14px style x minus y equals negative 3 minus open parentheses negative 1 half close parentheses equals negative 5 over 2 end style

 

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