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Pertanyaan

Diketahui begin mathsize 14px style open vertical bar a with rightwards arrow on top close vertical bar equals square root of 2 end style, begin mathsize 14px style open vertical bar b with rightwards arrow on top close vertical bar equals 3 end style dan begin mathsize 14px style open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar equals square root of 17 end style. Besar sudut yang dibentuk oleh vektor begin mathsize 14px style a with rightwards arrow on top space d a n space b with rightwards arrow on top end style adalah ....

  1. 30°

  2. 45°

  3. 60°

  4. 120°

  5. 135°

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa

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 end cell equals cell square root of 17 end cell 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 17 row cell open parentheses a with rightwards arrow on top minus b with rightwards arrow on top close parentheses times open parentheses a with rightwards arrow on top minus b with rightwards arrow on top close parentheses end cell equals 17 row cell a with rightwards arrow on top times a with rightwards arrow on top minus a with rightwards arrow on top times b with rightwards arrow on top minus b with rightwards arrow on top times a with rightwards arrow on top plus b with rightwards arrow on top times b with rightwards arrow on top end cell equals 17 row cell open vertical bar a with rightwards arrow on top close vertical bar open vertical bar a with rightwards arrow on top close vertical bar minus a with rightwards arrow on top times b with rightwards arrow on top minus a with rightwards arrow on top times b with rightwards arrow on top plus open vertical bar b with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar end cell equals 17 row cell open vertical bar a with rightwards arrow on top close vertical bar squared minus 2 a with rightwards arrow on top times b with rightwards arrow on top plus open vertical bar b with rightwards arrow on top close vertical bar squared end cell equals 17 row cell open parentheses square root of 2 close parentheses squared minus 2 a with rightwards arrow on top times b with rightwards arrow on top plus 3 squared end cell equals 17 row cell 2 minus 2 a with rightwards arrow on top times b with rightwards arrow on top plus 9 end cell equals 17 row cell 11 minus 2 a with rightwards arrow on top times b with rightwards arrow on top end cell equals 17 row cell negative 2 a with rightwards arrow on top times b with rightwards arrow on top end cell equals 6 row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell negative 3 end cell row blank blank blank end table end style

Misalkan besar sudut yang dibentuk oleh vektor begin mathsize 14px style a with rightwards arrow on top space d a n space b with rightwards arrow on top end style adalah α.
Maka didapatkan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator 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 fraction end cell row cell cos space alpha end cell equals cell fraction numerator negative 3 over denominator square root of 2 times 3 end fraction end cell row cell cos space alpha end cell equals cell fraction numerator negative 1 over denominator square root of 2 end fraction end cell row cell cos space alpha end cell equals cell fraction numerator negative 1 over denominator square root of 2 end fraction times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row cell cos space alpha end cell equals cell negative 1 half square root of 2 end cell row alpha equals cell 135 degree end cell end table end style

Jadi, jawaban yang tepat adalah E.

 

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