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Diketahui ∣ ∣ ​ a ∣ ∣ ​ = 2 ​ , ∣ ∣ ​ b ∣ ∣ ​ = 2 , dan ∣ a − b ∣ = 3 . Panjang vektor a + b = ...

Diketahui , dan . Panjang vektor  

  1. begin mathsize 14px style square root of 3 end style 

  2. begin mathsize 14px style square root of 5 end style 

  3. begin mathsize 14px style square root of 7 end style 

  4. begin mathsize 14px style 2 square root of 2 end style 

  5. begin mathsize 14px style 3 end style 

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D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

jawaban yang tepat adalah A.

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Pembahasan

Pertama, substitusikan pada hasil kuadrat dari . Sehingga, Jadi, jawaban yang tepat adalah A.

Pertama, substitusikan begin mathsize 14px style open vertical bar a with rightwards arrow on top close vertical bar equals square root of 2 comma space open vertical bar b with rightwards arrow on top close vertical bar equals 2 end style pada hasil kuadrat dari begin mathsize 14px style vertical line a with rightwards arrow on top minus b with rightwards arrow on top vertical line end style size 14px equals size 14px 3.

begin mathsize 14px style 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 3 squared end cell row 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 b with rightwards arrow on top close vertical bar plus open vertical bar b with rightwards arrow on top close vertical bar squared end cell equals 9 row cell open parentheses square root of 2 close parentheses squared minus 2 open vertical bar a with rightwards arrow on top b with rightwards arrow on top close vertical bar plus 2 squared end cell equals 9 row cell 2 minus 2 open vertical bar a with rightwards arrow on top b with rightwards arrow on top close vertical bar plus 4 end cell equals 9 row cell negative 2 open vertical bar a with rightwards arrow on top b with rightwards arrow on top close vertical bar end cell equals cell 9 minus 2 minus 4 end cell row cell negative 2 open vertical bar a with rightwards arrow on top b with rightwards arrow on top close vertical bar end cell equals 3 row cell open vertical bar a with rightwards arrow on top b with rightwards arrow on top close vertical bar end cell equals cell negative 3 over 2 end cell end table end style 

Sehingga,

begin mathsize 14px style 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 2 open vertical bar a with rightwards arrow on top b with rightwards arrow on top close vertical bar plus open vertical bar b with rightwards arrow on top close vertical bar squared end cell 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 parentheses square root of 2 close parentheses squared plus 2 open parentheses negative 3 over 2 close parentheses plus 2 squared end cell 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 2 minus 3 plus 4 end cell 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 3 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 plus-or-minus square root of 3 end cell end table end style 

Jadi, jawaban yang tepat adalah A.

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