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Pertanyaan

Diberikan OP = 3 p ​ + q ​ , OQ ​ = n p ​ − q ​ , dan OR = 3 p ​ + 5 q ​ . Jika P , Q dan R kolinear. Tentukan nilai n .

Diberikan , dan . Jika  dan  kolinear. Tentukan nilai .

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

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nilai adalah 3

nilai n adalah 3

Pembahasan

Diketahui , , dan . Jika , dan kolinear, maka: , dengan adalah sebuah konstanta. Sehingga: Dari kesamaan vektor tersebut didapat: Jadi, nilai adalah 3

Diketahui stack O P with rightwards arrow on top equals 3 p with rightwards arrow on top plus q with rightwards arrow on topstack O Q with rightwards arrow on top equals n p with rightwards arrow on top minus q with rightwards arrow on top, dan stack O R with rightwards arrow on top equals 3 p with rightwards arrow on top plus 5 q with rightwards arrow on top. Jika PQ dan R kolinear, maka:

P Q equals k cross times P R, dengan k adalah sebuah konstanta. Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell stack P Q with rightwards arrow on top end cell equals cell k cross times stack P R with rightwards arrow on top end cell row cell Q minus P end cell equals cell k cross times left parenthesis R minus P right parenthesis end cell row cell left parenthesis n p with rightwards arrow on top minus q with rightwards arrow on top right parenthesis minus left parenthesis 3 p with rightwards arrow on top plus q with rightwards arrow on top right parenthesis end cell equals cell k cross times open parentheses left parenthesis 3 p with rightwards arrow on top plus 5 q with rightwards arrow on top right parenthesis minus left parenthesis 3 p with rightwards arrow on top plus q with rightwards arrow on top right parenthesis close parentheses end cell row cell n p with rightwards arrow on top minus q with rightwards arrow on top minus 3 p with rightwards arrow on top minus q with rightwards arrow on top end cell equals cell k cross times open parentheses 3 p with rightwards arrow on top plus 5 q with rightwards arrow on top minus 3 p with rightwards arrow on top minus q with rightwards arrow on top close parentheses end cell row cell left parenthesis n minus 3 right parenthesis p with rightwards arrow on top minus 2 q with rightwards arrow on top end cell equals cell k cross times left parenthesis 4 q with rightwards arrow on top right parenthesis end cell row cell left parenthesis n minus 3 right parenthesis p with rightwards arrow on top minus 2 q with rightwards arrow on top end cell equals cell 0 plus 4 k q with rightwards arrow on top end cell end table 

Dari kesamaan vektor tersebut didapat:

table attributes columnalign right center left columnspacing 0px end attributes row cell n minus 3 end cell equals 0 row n equals 3 end table

Jadi, nilai n adalah 3

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