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Pertanyaan

a with rightwards harpoon with barb upwards on top equals open parentheses table row 4 row cell negative 5 end cell row 1 end table close parentheses space text dan end text space b with rightwards harpoon with barb upwards on top equals open parentheses table row 6 row 4 row cell negative 4 end cell end table close parentheses. Berapa sudut yang terbentuk antara dua vektor ?

L. Sibuea

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Pembahasan

Diketahui:

  • a with rightwards harpoon with barb upwards on top equals open parentheses table row 4 row cell negative 5 end cell row 1 end table close parentheses
  • b with rightwards harpoon with barb upwards on top equals open parentheses table row 6 row 4 row cell negative 4 end cell end table close parentheses

Ditanya:

Besar sudut kedua vektor left parenthesis alpha right parenthesis space ? 

Penyelesaian:

Langkah pertama: Tentukan perkalian vektor a dan b sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards harpoon with barb upwards on top space times space b with rightwards harpoon with barb upwards on top end cell equals cell open parentheses table row 4 row cell negative 5 end cell row 1 end table close parentheses space times space open parentheses table row 6 row 4 row cell negative 4 end cell end table close parentheses end cell row blank equals cell 4 space times space 6 space plus space minus 5 space times space 4 space plus space 1 space times space minus 4 end cell row blank equals cell 24 minus 20 minus 4 end cell row cell a with rightwards harpoon with barb upwards on top space times space b with rightwards harpoon with barb upwards on top end cell equals 0 end table 

Karena table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a with rightwards harpoon with barb upwards on top 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 times 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 cell b with rightwards harpoon with barb upwards 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 0 end table, maka tidak perlu untuk mencari panjang vektor  vektor a dan b.

Langkah kedua: Akan ditentukan besar sudut kedua vektor left parenthesis alpha right parenthesis sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell fraction numerator a with rightwards harpoon with barb upwards on top space times space b with rightwards harpoon with barb upwards on top over denominator open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar times open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar end fraction end cell row blank equals cell fraction numerator 0 over denominator open vertical bar a with rightwards harpoon with barb upwards on top close vertical bar times open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar end fraction end cell row cell cos space alpha end cell equals 0 row alpha equals cell 90 degree end cell end table 

Dengan demikian, besar sudut yang terbentuk antara dua vektor pada soal tersebut adalah 90 degree. 

 

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