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Diketahui koordinat titik , dan . Tentukan: b. ko...

Diketahui koordinat titik begin mathsize 14px style straight P left parenthesis 4 comma space 7 comma space minus 2 right parenthesis comma space straight Q left parenthesis 2 comma space minus 3 comma space 5 right parenthesis end style, dan Error converting from MathML to accessible text.. Tentukan:

b. koordinat S sehingga begin mathsize 14px style PS with rightwards arrow on top equals 3 PR with rightwards arrow on top minus PQ with rightwards arrow on top end style 

  1. ...   

  2. ...   

Jawaban:

Vektor posisi adalah vektor yang berpangkal di koordinat titik begin mathsize 14px style open parentheses x subscript 1 comma space y subscript 1 close parentheses end style dan berujung di suatu titik begin mathsize 14px style open parentheses x subscript 2 comma space y subscript 2 close parentheses end style. Cara menentukan vektor posisi yaitu dengan menghitung selisih dari koordinat titik ujung dan titik pangkal.

Koordinat titik P akan sama nilainya dengan vektor posisi begin mathsize 14px style p with rightwards arrow on top end style. Hal ini berlaku pula untuk koordinat titik Q, R, dan S.

Pada persamaan begin mathsize 14px style PS with rightwards arrow on top equals 3 PR with rightwards arrow on top minus PQ with rightwards arrow on top end style terdapat vektor posisi, perkalian vektor dengan skalar, dan selisih dua vektor posisi, Sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell PS with rightwards arrow on top end cell equals cell 3 PR with rightwards arrow on top minus PQ with rightwards arrow on top end cell row cell s with rightwards arrow on top minus p with rightwards arrow on top end cell equals cell 3 open parentheses r with rightwards arrow on top minus p with rightwards arrow on top close parentheses minus open parentheses q with rightwards arrow on top minus p with rightwards arrow on top close parentheses end cell row cell s with rightwards arrow on top minus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses end cell equals cell 3 times open square brackets open parentheses table row cell negative 1 end cell row 4 row 0 end table close parentheses minus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses close square brackets minus open square brackets open parentheses table row 2 row cell negative 3 end cell row 5 end table close parentheses minus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses close square brackets end cell row cell s with rightwards arrow on top minus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses end cell equals cell 3 times open parentheses table row cell negative 5 end cell row cell negative 3 end cell row 2 end table close parentheses minus open parentheses table row cell negative 2 end cell row cell negative 10 end cell row 7 end table close parentheses end cell row cell s with rightwards arrow on top minus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses end cell equals cell open parentheses table row cell negative 15 end cell row cell negative 9 end cell row 6 end table close parentheses minus open parentheses table row cell negative 2 end cell row cell negative 10 end cell row 7 end table close parentheses end cell row cell s with rightwards arrow on top minus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses end cell equals cell open parentheses table row cell negative 13 end cell row 1 row cell negative 1 end cell end table close parentheses end cell row cell s with rightwards arrow on top end cell equals cell open parentheses table row cell negative 13 end cell row 1 row cell negative 1 end cell end table close parentheses plus open parentheses table row 4 row 7 row cell negative 2 end cell end table close parentheses end cell row cell s with rightwards arrow on top end cell equals cell open parentheses table row cell negative 9 end cell row 8 row cell negative 3 end cell end table close parentheses end cell row blank blank blank end table end style 

Jadi, koordinat titik begin mathsize 14px style straight S left parenthesis negative 9 comma space 8 comma space minus 3 right parenthesis end style.

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