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Pertanyaan

Diketahui titik A ( 2 , 8 , 5 ) , B ( 1 , − 3 , 6 ) , dan C ( 3 , 7 , 7 ) . Jika vektor AB = p ​ , vektor BC = q ​ , vektor AC = r . Tentukan z = 3 p ​ − 2 q ​ + r .

Diketahui titik , , dan . Jika vektor , vektor , vektor . Tentukan .

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Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

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 z with rightwards arrow on top equals 3 p with rightwards arrow on top minus sign 2 q with rightwards arrow on top plus r with rightwards arrow on topequals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses negative sign 6 comma minus sign 54 comma 3 close parentheses end cell end table.

Pembahasan

Diketahui titik , , dan . Jika vektor , vektor , vektor . Diperoleh Diperoleh Jadi, .

Diketahui titik A left parenthesis 2 comma 8 comma 5 right parenthesis, B left parenthesis 1 comma minus sign 3 comma 6 right parenthesis, dan C left parenthesis 3 comma 7 comma 7 right parenthesis. Jika vektor AB with rightwards arrow on top equals p with rightwards arrow on top, vektor B with C yields on top equals q with rightwards arrow on top, vektor AC with rightwards arrow on top equals r with rightwards arrow on top. Diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell p with rightwards arrow on top end cell row cell p with rightwards arrow on top end cell equals cell B with rightwards arrow on top minus sign A with rightwards arrow on top end cell row cell p with rightwards arrow on top end cell equals cell open parentheses 1 comma minus sign 3 comma 6 close parentheses minus sign open parentheses 2 comma 8 comma 5 close parentheses end cell row cell p with rightwards arrow on top end cell equals cell open parentheses negative sign 1 comma minus sign 11 comma 1 close parentheses end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell B with C yields on top end cell equals cell q with rightwards arrow on top end cell row cell q with rightwards arrow on top end cell equals cell C with rightwards arrow on top minus sign B with rightwards arrow on top end cell row cell q with rightwards arrow on top end cell equals cell open parentheses 3 comma 7 comma 7 close parentheses minus sign open parentheses 1 comma minus sign 3 comma 6 close parentheses end cell row cell q with rightwards arrow on top end cell equals cell open parentheses 2 comma 10 comma 1 close parentheses end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell AC with rightwards arrow on top end cell equals cell r with rightwards arrow on top end cell row cell r with rightwards arrow on top end cell equals cell C with rightwards arrow on top minus sign A with rightwards arrow on top end cell row cell r with rightwards arrow on top end cell equals cell open parentheses 3 comma 7 comma 7 close parentheses minus sign open parentheses 2 comma 8 comma 5 close parentheses end cell row cell r with rightwards arrow on top end cell equals cell open parentheses 1 comma minus sign 1 comma 2 close parentheses end cell end table

Diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell z with rightwards arrow on top end cell equals cell 3 p with rightwards arrow on top minus sign 2 q with rightwards arrow on top plus r with rightwards arrow on top end cell row blank equals cell 3 open parentheses negative sign 1 comma minus sign 11 comma 1 close parentheses minus sign 2 open parentheses 2 comma 10 comma 1 close parentheses plus open parentheses 1 comma minus sign 1 comma 2 close parentheses end cell row blank equals cell open parentheses negative sign 3 comma minus sign 33 comma 3 close parentheses minus sign open parentheses 4 comma 20 comma 2 close parentheses plus open parentheses 1 comma minus sign 1 comma 2 close parentheses end cell row blank equals cell open parentheses negative sign 6 comma minus sign 54 comma 3 close parentheses end cell end table

Jadi, z with rightwards arrow on top equals 3 p with rightwards arrow on top minus sign 2 q with rightwards arrow on top plus r with rightwards arrow on topequals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses negative sign 6 comma minus sign 54 comma 3 close parentheses end cell end table.

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