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Jika koordinat titik , , dan . Hasil dari  adalah....

Jika koordinat titik begin mathsize 14px style A open parentheses 4 comma negative 2 close parentheses end stylebegin mathsize 14px style B open parentheses 1 comma 3 close parentheses end style, dan begin mathsize 14px style C left parenthesis negative 3 comma 2 right parenthesis end style. Hasil dari begin mathsize 14px style stack A B with rightwards arrow on top times stack B C with rightwards arrow on top end style adalah... .

  1. begin mathsize 14px style 17 end style 

  2. begin mathsize 14px style 7 end style 

  3. begin mathsize 14px style 5 end style 

  4. begin mathsize 14px style negative 7 end style 

  5. undefined 

Jawaban:

Diketahui koordinat titik begin mathsize 14px style A open parentheses 4 comma negative 2 close parentheses end stylebegin mathsize 14px style B open parentheses 1 comma 3 close parentheses end style, dan begin mathsize 14px style C open parentheses negative 3 comma 2 close parentheses end style. Suatu vektor posisi, elemennya sama dengan koordinat titik ujung. Misal, titik begin mathsize 14px style O end style adalah titik pangkal dengan koordinat begin mathsize 14px style O open parentheses 0 comma 0 close parentheses end style maka vektor posisi dari titik pangkal ke titik begin mathsize 14px style A open parentheses stack O A with rightwards arrow on top close parentheses end stylebegin mathsize 14px style B open parentheses stack O B with rightwards arrow on top close parentheses end style, dan begin mathsize 14px style C open parentheses stack O C with rightwards arrow on top close parentheses end style sebagai berikut.

  1. begin mathsize 14px style stack O A with rightwards arrow on top equals open parentheses table row 4 row cell negative 2 end cell end table close parentheses end style
  2. begin mathsize 14px style stack O B with rightwards arrow on top equals open parentheses table row 1 row 3 end table close parentheses end style
  3. begin mathsize 14px style stack O C with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row 2 end table close parentheses end style

Selanjutnya diperoleh vektor begin mathsize 14px style stack A B with rightwards arrow on top end style sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell stack O B with rightwards arrow on top minus stack O A with rightwards arrow on top end cell row blank equals cell open parentheses table row 1 row 3 end table close parentheses minus open parentheses table row 4 row cell negative 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 minus 4 end cell row cell 3 minus open parentheses negative 2 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 end cell row 5 end table close parentheses end cell end table end style

Vektor stack B C with rightwards arrow on top sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack B C with rightwards arrow on top end cell equals cell stack O C with rightwards arrow on top minus stack O B with rightwards arrow on top end cell row blank equals cell open parentheses table row cell negative 3 end cell row 2 end table close parentheses minus open parentheses table row 1 row 3 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 minus 1 end cell row cell 2 minus 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell row cell negative 1 end cell end table close parentheses end cell end table end style

Selanjutnya diperoleh begin mathsize 14px style stack A B with rightwards arrow on top times stack B C with rightwards arrow on top end style sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top times stack B C with rightwards arrow on top end cell equals cell open parentheses table row cell negative 3 end cell row 5 end table close parentheses times open parentheses table row cell negative 4 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses negative 3 close parentheses open parentheses negative 4 close parentheses plus 5 open parentheses negative 1 close parentheses end cell row blank equals cell 12 plus open parentheses negative 5 close parentheses end cell row blank equals 7 end table end style


Jadi, jawaban yang benar adalah B.

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