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Pertanyaan

Diketahui vektor – vektor sudut antara vektor adalah ….

Diketahui vektor – vektor begin mathsize 14px style a with rightwards arrow on top equals open parentheses 1 , 3 comma 3 close parentheses comma space b with rightwards arrow on top equals open parentheses 3 , 2 comma 1 close parentheses space text dan end text space c with rightwards arrow on top equals open parentheses 1 comma negative 5 , 0 close parentheses end style  sudut antara vektor begin mathsize 14px style open parentheses a with rightwards arrow on top minus b with rightwards arrow on top close parentheses space text dan end text space open parentheses a with rightwards arrow on top plus c with rightwards arrow on top close parentheses space end style adalah ….

  1. 30°

  2. 45°

  3. 60°

  4. 90°  

  5. 120°  

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R. Amalia

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

α =90° .

α=90°.

Pembahasan

Untuk mengetahui besar sudutnya gunakan rumus Sehingga α =90° .

begin mathsize 14px style a with rightwards arrow on top minus b with rightwards arrow on top equals open parentheses table row 1 row 3 row 3 end table close parentheses minus open parentheses table row 3 row 2 row 1 end table close parentheses equals open parentheses table row cell negative 2 end cell row 1 row 2 end table close parentheses a with rightwards arrow on top plus c with rightwards arrow on top equals open parentheses table row 1 row 3 row 3 end table close parentheses plus open parentheses table row 1 row cell negative 5 end cell row 0 end table close parentheses equals open parentheses table row 2 row cell negative 2 end cell row 3 end table close parentheses end style    

Untuk mengetahui besar sudutnya gunakan rumus

begin mathsize 14px style cos invisible function application alpha equals fraction numerator open parentheses a with rightwards arrow on top minus b with rightwards arrow on top close parentheses. open parentheses a with rightwards arrow on top plus c with rightwards arrow on top close parentheses over denominator open vertical bar a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar. open vertical bar a with rightwards arrow on top plus c with rightwards arrow on top close vertical bar end fraction cos invisible function application alpha equals fraction numerator open parentheses table row cell negative 2 end cell row 1 row 2 end table close parentheses. open parentheses table row 2 row cell negative 2 end cell row 3 end table close parentheses over denominator square root of open parentheses negative 2 close parentheses squared plus 1 squared plus 2 squared end root. square root of 2 squared plus open parentheses negative 2 close parentheses squared plus 3 squared end root end fraction equals 0 end style         

Sehingga α=90°.

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Diberikan tiga buah vektor seperti berikut. Jika besar vektor a , b , dan c berturut-turut adalah 5, 12, dan 13 maka a . b = … .

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