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Pertanyaan

Diketahui vektor a with bar on top dan b with bar on top dengan open vertical bar a with bar on top close vertical bar equals 1 dan open vertical bar b with bar on top close vertical bar equals square root of 2. Jika a. b equals 1  maka besar sudut yang dibentuk vektor a with bar on top dan b with bar on top equals... 

  1. 30 to the power of ring operator 

  2. 45 to the power of ring operator 

  3. 60 to the power of ring operator 

  4. 75 to the power of ring operator 

  5. 90 to the power of ring operator 

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Diketahui:

  • open vertical bar a with rightwards arrow on top close vertical bar equals 1
  • open vertical bar b with rightwards arrow on top close vertical bar equals square root of 2
  • a. b equals 1

Ingat!

Perkalian skalar vektor a with rightwards arrow on top dengan vektor b with rightwards arrow on top open parentheses table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell b with rightwards arrow on top end cell end table close parentheses didefinisikan sebagai hasil kali panjang vektor a with rightwards arrow on top dan panjang vektor b with rightwards arrow on top dengan kosinus sudut yang diapit oleh vektor a with rightwards arrow on top dan vektor b with rightwards arrow on top atau table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell b with rightwards arrow on top 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 cell stack open vertical bar a close vertical bar with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open vertical bar 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 blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank alpha end table.

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top. b with rightwards arrow on top end cell equals cell stack open vertical bar a close vertical bar with rightwards arrow on top open vertical bar b with rightwards arrow on top close vertical bar space cos space alpha end cell row 1 equals cell 1 cross times square root of 2 cross times cos space alpha end cell row 1 equals cell square root of 2 cos space alpha end cell row cell cos space alpha end cell equals cell fraction numerator 1 over denominator square root of 2 end fraction cross 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 1 half square root of 2 end cell row alpha equals cell 45 degree end cell end table 


Jadi, jawaban yang tepat adalah B.

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