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Diketahui , , dan  sudut antara vektor  dan . Nilai  adalah ...

Pertanyaan

Diketahui begin mathsize 14px style p with bar on top equals i plus 2 j end stylebegin mathsize 14px style q with bar on top equals 4 i plus 2 j end style, dan begin mathsize 14px style straight theta end style sudut antara vektor begin mathsize 14px style p with bar on top end style dan begin mathsize 14px style q with bar on top end style. Nilai begin mathsize 14px style sin space straight theta end style adalah ...

  1. begin mathsize 14px style 3 over 5 end style 

  2. begin mathsize 14px style 3 over 4 end style 

  3. begin mathsize 14px style 4 over 5 end style 

  4. begin mathsize 14px style 9 over 16 end style 

  5. begin mathsize 14px style 5 over 13 end style 

Pembahasan Soal:

Berdasarkan konsep sudut antara dua vektor maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space theta end cell equals cell fraction numerator p with bar on top times q with bar on top over denominator open vertical bar p with bar on top close vertical bar times open vertical bar q with bar on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses table row 1 row 2 end table close parentheses times open parentheses table row 4 row 2 end table close parentheses over denominator square root of 1 squared plus 2 squared end root times square root of 4 squared plus 2 squared end root end fraction end cell row blank equals cell fraction numerator 4 plus 4 over denominator square root of 5 times square root of 20 end fraction end cell row blank equals cell fraction numerator 8 over denominator square root of 100 end fraction end cell row blank equals cell 8 over 10 end cell row blank equals cell 4 over 5 end cell end table end style 

Oleh karena definisi cos adalah 

begin mathsize 14px style cos space straight theta equals samping over miring equals 4 over 5 end style  

maka berdasarkan teorema Pythagoras diperoleh sisi depan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sisi space depan end cell equals cell square root of 5 squared minus 4 squared end root end cell row blank equals cell square root of 25 minus 16 end root end cell row blank equals cell square root of 9 end cell row blank equals 3 end table end style 

sehingga diperoleh nilai:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight theta end cell equals cell depan over miring end cell row blank equals cell 3 over 5 end cell end table end style 

Oleh karena itu, jawaban yang benar adalah A.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 Maret 2021

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