Diketahui a+b=i−j​+4k dan ∣∣​a+b∣∣​=14​. Hasil dari a∙b adalah ....

Pertanyaan

Diketahui a with rightwards arrow on top plus b with rightwards arrow on top equals i with hat on top minus j with hat on top plus 4 k with hat on top dan open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar equals square root of 14. Hasil dari a with rightwards arrow on top bullet b with rightwards arrow on top adalah ....

  1. 4 square root of 14 

  2. 2 square root of 14 

  3. square root of 14

  4. 1 

  5. 0 

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah D.

Apabila diketahui a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell row cell a subscript 3 end cell end table close parentheses dan b with rightwards arrow on top equals open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell row cell b subscript 3 end cell end table close parentheses, maka berlaku :

  • open vertical bar a with rightwards arrow on top close vertical bar equals square root of open parentheses a subscript 1 close parentheses squared plus open parentheses a subscript 2 close parentheses squared plus open parentheses a subscript 3 close parentheses squared end root 
  • open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar squared equals open vertical bar a with rightwards arrow on top close vertical bar squared plus open vertical bar b with rightwards arrow on top close vertical bar squared plus 2 open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar 
  • open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar squared equals open vertical bar a with rightwards arrow on top close vertical bar squared plus open vertical bar b with rightwards arrow on top close vertical bar squared minus 2 open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar 

Diketahui bahwa a with rightwards arrow on top plus b with rightwards arrow on top equals i with hat on top minus j with hat on top plus 4 k with hat on top equals open parentheses 1 comma space minus 1 comma space 4 close parentheses maka open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar diperoleh :

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar end cell equals cell square root of 1 squared plus open parentheses negative 1 close parentheses squared plus 4 squared end root end cell row blank equals cell square root of 1 plus 1 plus 16 end root end cell row blank equals cell square root of 18 end cell end table 

Karena nilai table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar end cell equals cell square root of 18 end cell end table maka diasumsikan open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar equals square root of 14 pada soal adalah open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar equals square root of 14.

Jika kita aplikasikan rumus ke-2 dan ke-3 di atas maka diperoleh :

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar squared end cell equals cell open vertical bar a with rightwards arrow on top close vertical bar squared plus open vertical bar b with rightwards arrow on top close vertical bar squared plus 2 open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar end cell row cell open parentheses square root of 18 close parentheses squared end cell equals cell open vertical bar a with rightwards arrow on top close vertical bar squared plus open vertical bar b with rightwards arrow on top close vertical bar squared plus 2 open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar end cell row 18 equals cell open vertical bar a with rightwards arrow on top close vertical bar squared plus open vertical bar b with rightwards arrow on top close vertical bar squared plus 2 open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar space horizontal ellipsis space open parentheses bold i close parentheses end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar squared end cell equals cell open vertical bar a with rightwards arrow on top close vertical bar squared plus open vertical bar b with rightwards arrow on top close vertical bar squared minus 2 open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar end cell row cell open parentheses square root of 14 close parentheses squared end cell equals cell open vertical bar a with rightwards arrow on top close vertical bar squared plus open vertical bar b with rightwards arrow on top close vertical bar squared minus 2 open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar end cell row 14 equals cell open vertical bar a with rightwards arrow on top close vertical bar squared plus open vertical bar b with rightwards arrow on top close vertical bar squared minus 2 open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar space horizontal ellipsis space open parentheses bold ii close parentheses end cell end table 

Kita eliminasi kedua persamaan tersebut diperoleh :

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell table row cell up diagonal strike open vertical bar a with rightwards arrow on top close vertical bar squared plus open vertical bar b with rightwards arrow on top close vertical bar squared end strike plus 2 open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar equals 18 end cell row cell up diagonal strike open vertical bar a with rightwards arrow on top close vertical bar squared plus open vertical bar b with rightwards arrow on top close vertical bar squared end strike minus 2 open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar space equals 14 space minus end cell row cell 4 open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar equals 4 end cell row cell open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar equals 4 over 4 end cell row cell open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar equals 1 end cell row cell a with rightwards arrow on top bullet b with rightwards arrow on top equals 1 end cell end table end cell end table 

Dengan demikian, hasil dari a with rightwards arrow on top bullet b with rightwards arrow on top adalah 1.

Oleh karena itu, jawaban yang benar adalah D.

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