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Jika P , Q , dan R berturut-turut titik tengah BC , CA , dan AB dari △ ABC serta a , b , dan c merupakan vektor posisi dari titik A , B , dan C , maka AP + BQ ​ + CR = …

Jika  berturut-turut titik tengah  dari  serta  merupakan vektor posisi dari titik , maka  

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

  2. begin mathsize 14px style p with rightwards arrow on top plus r with rightwards arrow on top end style 

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

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

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

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D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Vektor dapat ditentukan sebagai berikut. Vektor adalah sebagai berikut. Hasil dari penjumlahan vektor tersebut adalah sebagai berikut. Oleh karena itu, jawaban yang tepat adalah E.

Vektor begin mathsize 14px style stack B C with rightwards arrow on top comma space stack C A with rightwards arrow on top comma space text dan end text space stack A B with rightwards arrow on top end style dapat ditentukan 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 c with rightwards arrow on top minus b end cell row cell stack C A with rightwards arrow on top end cell equals cell stack O A with rightwards arrow on top minus stack O C with rightwards arrow on top end cell row blank equals cell a with rightwards arrow on top minus c with rightwards arrow on top end cell 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 b with rightwards arrow on top minus a with rightwards arrow on top end cell end table end style

Vektor begin mathsize 14px style stack A P with rightwards arrow on top comma space stack B Q with rightwards arrow on top comma space text dan end text space stack C R with rightwards arrow on top end style adalah sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack A P with rightwards arrow on top end cell equals cell stack A B with rightwards arrow on top plus stack B P with rightwards arrow on top end cell row blank equals cell b with rightwards arrow on top minus a with rightwards arrow on top plus 1 half open parentheses c with rightwards arrow on top minus b with rightwards arrow on top close parentheses end cell row blank equals cell negative a with rightwards arrow on top plus 1 half b with rightwards arrow on top plus 1 half c with rightwards arrow on top end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack B Q with rightwards arrow on top end cell equals cell stack B C with rightwards arrow on top plus stack C Q with rightwards arrow on top end cell row blank equals cell c with rightwards arrow on top minus b with rightwards arrow on top plus 1 half open parentheses a with rightwards arrow on top minus c with rightwards arrow on top close parentheses end cell row blank equals cell 1 half a with rightwards arrow on top minus b with rightwards arrow on top plus 1 half c with rightwards arrow on top end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack C R with rightwards arrow on top end cell equals cell stack C A with rightwards arrow on top plus stack A R with rightwards arrow on top end cell row blank equals cell a with rightwards arrow on top minus c with rightwards arrow on top plus 1 half open parentheses b with rightwards arrow on top minus a with rightwards arrow on top close parentheses end cell row blank equals cell 1 half a with rightwards arrow on top plus 1 half b with rightwards arrow on top minus c with rightwards arrow on top end cell end table end style

Hasil dari penjumlahan vektor tersebut adalah sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack A P with rightwards arrow on top plus stack B Q with rightwards arrow on top plus stack C R with rightwards arrow on top end cell row blank equals cell open parentheses negative a with rightwards arrow on top plus 1 half b with rightwards arrow on top plus 1 half c with rightwards arrow on top close parentheses plus open parentheses 1 half a with rightwards arrow on top minus b with rightwards arrow on top plus 1 half c with rightwards arrow on top close parentheses end cell row blank blank cell plus open parentheses 1 half a with rightwards arrow on top plus 1 half b with rightwards arrow on top minus c with rightwards arrow on top close parentheses end cell row blank equals 0 row blank equals cell O with rightwards arrow on top end cell end table end style

Oleh karena itu, jawaban yang tepat adalah E.

 

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