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Pertanyaan

Jika nilai ∣ ∣ ​ a ∣ ∣ ​ = 4 , ∣ ∣ ​ b ∣ ∣ ​ = 6 , dan ∣ ∣ ​ a + b ∣ ∣ ​ = 8 , nilai ∣ ∣ ​ a − b ∣ ∣ ​ adalah....

Jika nilai , , dan , nilai  adalah....

  1. 2

  2. 4

  3. 2 square root of 6

  4. 2 square root of 10

  5. 2 square root of 14

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E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

jawaban yang benar adalah D.

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Pembahasan

Diketahui: Sehingga Selanjutnya Karena panjang vektor selalu positif maka nilai . Oleh karena itu, jawaban yang benar adalah D .

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top close vertical bar end cell equals 4 row cell open vertical bar b with rightwards arrow on top close vertical bar end cell equals 6 row cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar end cell equals 8 end table

Sehingga

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 8 squared end cell row cell open vertical bar a 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 cos space alpha plus open vertical bar b with rightwards arrow on top close vertical bar end cell equals 64 row cell 4 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 cos space alpha plus 6 squared end cell equals 64 row cell 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 cos space alpha end cell equals cell 64 minus 16 minus 36 end cell row cell 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 cos space alpha end cell equals 12 end table

Selanjutnya

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 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 cos space alpha plus open vertical bar b with rightwards arrow on top close vertical bar end cell row blank equals cell 4 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 cos space alpha plus 6 squared end cell row blank equals cell 16 minus 12 plus 36 end cell row blank equals 40 row cell open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar end cell equals cell plus-or-minus square root of 40 end cell row blank equals cell plus-or-minus 2 square root of 10 end cell end table

Karena panjang vektor selalu positif maka nilai table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 10 end cell end table.

Oleh karena itu, jawaban yang benar adalah D.

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