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Pertanyaan

Diketahui ∣ ∣ ​ a ∣ ∣ ​ = 6 , ∣ ∣ ​ b ∣ ∣ ​ = 4 dan ∣ ∣ ​ a + b ∣ ∣ ​ = 2 3 ​ , maka ∣ a − b ∣ adalah ...​​​

Diketahui  dan , maka  adalah ...​​​  

  1. begin mathsize 14px style 5 end style 

  2. begin mathsize 14px style 7 end style

  3. begin mathsize 14px style 2 square root of 23 end style

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

  5. begin mathsize 14px style 6 square root of 3 end style

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C

jawaban yang tepat adalah C

Pembahasan

Karena panjang vektor tidak mungkin negatif maka Jadi, jawaban yang tepat adalah C

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell vertical line a with rightwards arrow on top plus b with rightwards arrow on top vertical line 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 vertical line a with rightwards arrow on top vertical line open vertical bar b with rightwards arrow on top close vertical bar cos space theta end cell row cell open parentheses 2 square root of 3 close parentheses squared end cell equals cell 6 squared plus 4 squared plus 2 vertical line a with rightwards arrow on top vertical line open vertical bar b with rightwards arrow on top close vertical bar cos space theta end cell row 12 equals cell 36 plus 16 plus 2 vertical line a with rightwards arrow on top vertical line open vertical bar b with rightwards arrow on top close vertical bar cos space theta end cell row cell 12 minus 52 end cell equals cell 2 vertical line a with rightwards arrow on top vertical line vertical line b with rightwards arrow on top vertical line cos space theta end cell row cell negative 40 end cell equals cell 2 vertical line a with rightwards arrow on top vertical line vertical line b with rightwards arrow on top vertical line cos space theta end cell row blank blank blank end table end style

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line a with rightwards arrow on top minus b with rightwards arrow on top vertical line squared end cell equals cell vertical line a with rightwards arrow on top vertical line squared plus vertical line b with rightwards arrow on top vertical line squared minus 2 vertical line a with rightwards arrow on top vertical line vertical line b with rightwards arrow on top vertical line cos space theta end cell row blank equals cell 6 squared plus 4 squared minus 2 left parenthesis negative 40 right parenthesis end cell row blank equals cell 36 plus 16 plus 40 end cell row blank equals 92 row blank blank blank 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 92 end cell row blank equals cell plus-or-minus 2 square root of 23 end cell row blank blank blank row blank blank blank end table end style

Karena panjang vektor tidak mungkin negatif maka  begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell vertical line a with rightwards arrow on top minus b with rightwards arrow on top vertical line 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 23 end cell end table end style 

Jadi, jawaban yang tepat adalah C

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