Roboguru

Vektor posisi A, B, dan C terhadap titik O secara berturut-turut adalah a=u+v+2w, b=3u+4v+w, dan c=9u+13v−2w. Jika titik A, B, dan C segaris, maka AB:BC adalah ....

Pertanyaan

Vektor posisi A, B, dan C terhadap titik O secara berturut-turut adalah begin mathsize 14px style straight a with rightwards arrow on top equals straight u with rightwards arrow on top plus straight v with rightwards arrow on top plus 2 straight w with rightwards arrow on top end stylebegin mathsize 14px style straight b with rightwards arrow on top equals 3 straight u with rightwards arrow on top plus 4 straight v with rightwards arrow on top plus straight w with rightwards arrow on top end style, dan begin mathsize 14px style straight c with rightwards arrow on top equals 9 straight u with rightwards arrow on top plus 13 straight v with rightwards arrow on top minus 2 straight w with rightwards arrow on top end style. Jika titik A, B, dan C segaris, maka begin mathsize 14px style AB with rightwards arrow on top colon BC with rightwards arrow on top end style adalah ....

  1. begin mathsize 14px style 1 colon 1 end style 

  2. begin mathsize 14px style 1 colon 2 end style 

  3. begin mathsize 14px style 1 colon 3 end style 

  4. begin mathsize 14px style 2 colon 1 end style 

  5. begin mathsize 14px style 3 colon 1 end style 

Pembahasan:

Perhatikan bahwa,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell OB with rightwards arrow on top minus OA with rightwards arrow on top end cell row blank equals cell straight b with rightwards arrow on top minus straight a with rightwards arrow on top end cell row blank equals cell open parentheses 3 straight u with rightwards arrow on top plus 4 straight v with rightwards arrow on top plus straight w with rightwards arrow on top close parentheses minus open parentheses straight u with rightwards arrow on top plus straight v with rightwards arrow on top plus 2 straight w with rightwards arrow on top close parentheses end cell row blank equals cell 3 straight u with rightwards arrow on top plus 4 straight v with rightwards arrow on top plus straight w with rightwards arrow on top minus straight u with rightwards arrow on top minus straight v with rightwards arrow on top minus 2 straight w with rightwards arrow on top end cell row blank equals cell 2 straight u with rightwards arrow on top plus 3 straight v with rightwards arrow on top minus straight w with rightwards arrow on top end cell end table end style  

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell BC with rightwards arrow on top end cell equals cell OC with rightwards arrow on top minus OB with rightwards arrow on top end cell row blank equals cell straight c with rightwards arrow on top minus straight b with rightwards arrow on top end cell row blank equals cell open parentheses 9 straight u with rightwards arrow on top plus 13 straight v with rightwards arrow on top minus 2 straight w with rightwards arrow on top close parentheses minus open parentheses 3 straight u with rightwards arrow on top plus 4 straight v with rightwards arrow on top plus straight w with rightwards arrow on top close parentheses end cell row blank equals cell 9 straight u with rightwards arrow on top plus 13 straight v with rightwards arrow on top minus 2 straight w with rightwards arrow on top minus 3 straight u with rightwards arrow on top minus 4 straight v with rightwards arrow on top minus straight w with rightwards arrow on top end cell row blank equals cell 6 straight u with rightwards arrow on top plus 9 straight v with rightwards arrow on top minus 3 straight w with rightwards arrow on top end cell row blank equals cell 3 open parentheses 2 straight u with rightwards arrow on top plus 3 straight v with rightwards arrow on top minus straight w with rightwards arrow on top close parentheses end cell row blank equals cell 3 AB with rightwards arrow on top end cell end table end style 

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell BC with rightwards arrow on top end cell equals cell 3 AB with rightwards arrow on top end cell row cell fraction numerator BC with rightwards arrow on top over denominator AB with rightwards arrow on top end fraction end cell equals cell 3 over 1 end cell end table end style 

Maka begin mathsize 14px style BC with rightwards arrow on top colon AB with rightwards arrow on top equals 3 colon 1 end style. Akibatnya, begin mathsize 14px style AB with rightwards arrow on top colon BC with rightwards arrow on top equals 1 colon 3 end style.

Jadi, jawaban yang tepat adalah C.space space  

Jawaban terverifikasi

Dijawab oleh:

S. Nur

Terakhir diupdate 25 November 2021

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