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Pertanyaan

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

Vektor posisi A, B, dan C terhadap titik O secara berturut-turut adalah , , dan . Jika titik A, B, dan C segaris, maka  adalah ....

  1. 1 : 3

  2. 1 : 2

  3. 1 : 1

  4. 2 : 1

  5. 3 : 1

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F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

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Pembahasan

Perhatikan bahwa dan Sehinga Maka . Akibatnya,

Perhatikan bahwa

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 b with rightwards arrow on top minus a with rightwards arrow on top end cell row blank equals cell open parentheses 3 u with rightwards arrow on top plus 4 v with rightwards arrow on top plus w with rightwards arrow on top close parentheses minus open parentheses u with rightwards arrow on top plus v with rightwards arrow on top plus 2 w with rightwards arrow on top close parentheses end cell row blank equals cell 3 u with rightwards arrow on top plus 4 v with rightwards arrow on top plus w with rightwards arrow on top minus u with rightwards arrow on top minus v with rightwards arrow on top minus 2 w with rightwards arrow on top end cell row blank equals cell 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top minus 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 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 with rightwards arrow on top end cell row blank equals cell open parentheses 9 u with rightwards arrow on top plus 13 v with rightwards arrow on top minus 2 w with rightwards arrow on top close parentheses minus open parentheses 3 u with rightwards arrow on top plus 4 v with rightwards arrow on top plus w with rightwards arrow on top close parentheses end cell row blank equals cell 9 u with rightwards arrow on top plus 13 v with rightwards arrow on top minus 2 w with rightwards arrow on top minus 3 u with rightwards arrow on top minus 4 v with rightwards arrow on top minus w with rightwards arrow on top end cell row blank equals cell 6 u with rightwards arrow on top plus 9 v with rightwards arrow on top minus 3 w with rightwards arrow on top end cell row blank equals cell 3 open parentheses 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top minus w with rightwards arrow on top close parentheses end cell row blank equals cell 3 stack A B with rightwards arrow on top end cell end table end style

Sehinga

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 3 stack A B with rightwards arrow on top end cell row cell fraction numerator stack B C with rightwards arrow on top over denominator stack A B 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 stack B C with rightwards arrow on top colon stack A B with rightwards arrow on top equals 3 colon 1 end style. Akibatnya, begin mathsize 14px style stack A B with rightwards arrow on top colon stack B C with rightwards arrow on top equals 1 colon 3 end style

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Perhatikan gambar berikut ini Diketahui titik C merupakan titik tengah OB. Jika OB = p ​ , A B = q ​ , dan AC diperpanjang hingga D dengan AC : CD = 5 : 2, maka B D = ...

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