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Jika 2 AB + p ​ + CA = DB + CB dan CD + p ​ , maka hasil dari q ​ − BA adalah...

Jika  dan , maka hasil dari  adalah ...

  1. begin mathsize 14px style DB with rightwards arrow on top end style 

  2. begin mathsize 14px style BD with rightwards arrow on top end style 

  3. begin mathsize 14px style CA with rightwards arrow on top end style 

  4. begin mathsize 14px style CB with rightwards arrow on top end style 

  5. begin mathsize 14px style BC with rightwards arrow on top end style 

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

jawaban yang tepat adalah D.

Pembahasan

Ingat kembali jika terdapat suatu vektor , maka vektor yang berlawanan arah dari adalah . Kemudian, ingat pula bahwa vektor yang dimulai dari berakhir di titik yang samadapat disebut sebagai vektor nol, atau . Sekarang, perhatikan perhitungan berikut ini! Akibatnya, didapat hasil sebagai berikut. Dengan demikian, diperoleh hasil sebagai berikut. Jadi, jawaban yang tepat adalah D.

Ingat kembali jika terdapat suatu vektor XY with rightwards arrow on top, maka vektor yang berlawanan arah dari XY with rightwards arrow on top adalah YX with rightwards arrow on top equals negative XY with rightwards arrow on top. Kemudian, ingat pula bahwa vektor yang dimulai dari berakhir di titik yang sama dapat disebut sebagai vektor nol, atau XX with rightwards arrow on top equals 0 with rightwards arrow on top.

Sekarang, perhatikan perhitungan berikut ini!

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 AB with rightwards arrow on top plus p with rightwards arrow on top plus CA with rightwards arrow on top end cell equals cell DB with rightwards arrow on top plus CB with rightwards arrow on top end cell row cell p with rightwards arrow on top end cell equals cell DB with rightwards arrow on top plus CB with rightwards arrow on top minus 2 AB with rightwards arrow on top minus CA with rightwards arrow on top end cell row cell p with rightwards arrow on top end cell equals cell DB with rightwards arrow on top plus CB with rightwards arrow on top minus AB with rightwards arrow on top minus AB with rightwards arrow on top minus CA with rightwards arrow on top end cell row cell p with rightwards arrow on top end cell equals cell DB with rightwards arrow on top plus CB with rightwards arrow on top minus open parentheses negative BA with rightwards arrow on top close parentheses minus open parentheses negative BA with rightwards arrow on top close parentheses minus open parentheses negative AC with rightwards arrow on top close parentheses end cell row cell p with rightwards arrow on top end cell equals cell DB with rightwards arrow on top plus CB with rightwards arrow on top plus BA with rightwards arrow on top plus BA with rightwards arrow on top plus AC with rightwards arrow on top end cell row cell p with rightwards arrow on top end cell equals cell DB with rightwards arrow on top plus BA with rightwards arrow on top plus CB with rightwards arrow on top plus BA with rightwards arrow on top plus AC with rightwards arrow on top end cell row cell p with rightwards arrow on top end cell equals cell open parentheses DB with rightwards arrow on top plus BA with rightwards arrow on top close parentheses plus open parentheses CB with rightwards arrow on top plus BA with rightwards arrow on top plus AC with rightwards arrow on top close parentheses end cell row cell p with rightwards arrow on top end cell equals cell DA with rightwards arrow on top plus CC with rightwards arrow on top end cell row cell p with rightwards arrow on top end cell equals cell DA with rightwards arrow on top plus 0 with rightwards arrow on top end cell row cell p with rightwards arrow on top end cell equals cell DA with rightwards arrow on top end cell end table

Akibatnya, didapat hasil sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell q with rightwards arrow on top end cell equals cell CD with rightwards arrow on top plus p with rightwards arrow on top end cell row cell q with rightwards arrow on top end cell equals cell CD with rightwards arrow on top plus DA with rightwards arrow on top end cell row cell q with rightwards arrow on top end cell equals cell CA with rightwards arrow on top end cell end table 

Dengan demikian, diperoleh hasil sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell q with rightwards arrow on top minus BA with rightwards arrow on top end cell equals cell CA with rightwards arrow on top minus BA with rightwards arrow on top end cell row blank equals cell CA with rightwards arrow on top minus open parentheses negative AB with rightwards arrow on top close parentheses end cell row blank equals cell CA with rightwards arrow on top plus AB with rightwards arrow on top end cell row blank equals cell CB with rightwards arrow on top end cell end table 

Jadi, jawaban yang tepat adalah D.

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