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Pertanyaan

Vektor posisi A , B dan C adalah 2 a − b , t a + b dan 12 a + 4 b . Hitunglah nilai t agar , dan kolinear.

Vektor posisi ,  dan  adalah  dan . Hitunglah nilai  agar A, B dan C kolinear.

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

nilai agar , dan kolinear adalah

 nilai t agar A, B dan C kolinear adalah negative 18 

Pembahasan

Diketahui vektor posisi , dan adalah , dan . , dan kolinear, maka berlaku , sehingga: Dari kesamaan vektor posisi , didapat: Perhatikan kesamaan vektor posisi , maka: Jadi,nilai agar , dan kolinear adalah

Diketahui vektor posisi A, B dan C adalah 2 a with rightwards arrow on top minus b with rightwards arrow on topt a with rightwards arrow on top plus b with rightwards arrow on top dan 12 a with rightwards arrow on top plus 4 b with rightwards arrow on top. A, B dan C kolinear, maka berlaku table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack A B with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank k end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack B C with rightwards arrow on top end cell end table, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell k cross times stack B C with rightwards arrow on top end cell row cell B minus A end cell equals cell k cross times open parentheses C minus B close parentheses end cell row cell open parentheses t a with rightwards arrow on top plus b with rightwards arrow on top close parentheses minus open parentheses 2 a with rightwards arrow on top minus b with rightwards arrow on top close parentheses end cell equals cell k cross times open parentheses open parentheses 12 a with rightwards arrow on top plus 4 b with rightwards arrow on top close parentheses minus open parentheses t a with rightwards arrow on top plus b with rightwards arrow on top close parentheses close parentheses end cell row cell t a with rightwards arrow on top plus b with rightwards arrow on top minus 2 a with rightwards arrow on top plus b with rightwards arrow on top end cell equals cell k cross times open parentheses 12 a with rightwards arrow on top plus 4 b with rightwards arrow on top minus t a with rightwards arrow on top minus b with rightwards arrow on top close parentheses end cell row cell left parenthesis t minus 2 right parenthesis a with rightwards arrow on top plus 2 b with rightwards arrow on top end cell equals cell k left parenthesis 12 minus t right parenthesis a with rightwards arrow on top minus 3 k b with rightwards arrow on top end cell end table 

Dari kesamaan vektor posisi b with rightwards arrow on top, didapat:

2 equals negative 3 k k equals negative 2 over 3

Perhatikan kesamaan vektor posisi a with rightwards arrow on top, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell t minus 2 end cell equals cell k left parenthesis 12 minus t right parenthesis end cell row cell t minus 2 end cell equals cell negative 2 over 3 left parenthesis 12 minus t right parenthesis end cell row cell 3 left parenthesis t minus 2 right parenthesis end cell equals cell negative 2 left parenthesis 12 minus t right parenthesis end cell row cell 3 t minus 6 end cell equals cell negative 24 plus 2 t end cell row cell 3 t minus 2 t end cell equals cell negative 24 plus 6 end cell row t equals cell negative 18 end cell end table

Jadi, nilai t agar A, B dan C kolinear adalah negative 18 

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Faiz Aqil Fakhri

Jawaban tidak sesuai Kak kenapa 4b-b= -3b? yang di bagian "k ( 12a + 4b - ta - b)" kok jadi -3kb?

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