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Pertanyaan

Diketahui p ​ = 2 a + 3 b , q ​ = 4 a − b , dan r = h a + ( 3 h + k ) b dengan h dan k konstanta, a dan b tidak sejajar. Hitunglah nilai dan saat 2 p ​ = 3 q ​ − 4 r .

Diketahui , dan  dengan  dan  konstanta,  dan  tidak sejajar. Hitunglah nilai h dan k saat .

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I. Sutiawan

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Mahasiswa/Alumni Universitas Pasundan

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nilai dan saat adalah dan

nilai h dan k saat 2 p with rightwards arrow on top equals 3 q with rightwards arrow on top minus 4 r with rightwards arrow on top adalah h equals 2 dan k equals negative 33 over 4 

Pembahasan

Diketahui , , dan .Jika , maka: Dari kesamaan vektor tersebut didapat: Jadi, nilai dan saat adalah dan

Diketahui p with rightwards arrow on top equals 2 a with rightwards arrow on top plus 3 b with rightwards arrow on topq with rightwards arrow on top equals 4 a with rightwards arrow on top minus b with rightwards arrow on top, dan r with rightwards arrow on top equals h a with rightwards arrow on top plus left parenthesis 3 h plus k right parenthesis b with rightwards arrow on top. Jika 2 p with rightwards arrow on top equals 3 q with rightwards arrow on top minus 4 r with rightwards arrow on top, maka:

2 p with rightwards arrow on top equals 3 q with rightwards arrow on top minus 4 r with rightwards arrow on top 2 open parentheses 2 a with rightwards arrow on top plus 3 b with rightwards arrow on top close parentheses equals 3 open parentheses 4 a with rightwards arrow on top minus b with rightwards arrow on top close parentheses minus 4 open parentheses h a with rightwards arrow on top plus left parenthesis 3 h plus k right parenthesis b with rightwards arrow on top close parentheses 4 a with rightwards arrow on top plus 6 b with rightwards arrow on top equals 12 a with rightwards arrow on top minus 3 b with rightwards arrow on top minus 4 h a with rightwards arrow on top minus 12 h b with rightwards arrow on top minus 4 k b with rightwards arrow on top 4 a with rightwards arrow on top plus 6 b with rightwards arrow on top equals left parenthesis 12 minus 4 h right parenthesis a with rightwards arrow on top plus left parenthesis negative 3 minus 12 h minus 4 k right parenthesis b with rightwards arrow on top   

Dari kesamaan vektor tersebut didapat:

table attributes columnalign right center left columnspacing 0px end attributes row 4 equals cell 12 minus 4 h end cell row cell 4 h end cell equals cell 12 minus 4 end cell row cell 4 h end cell equals 8 row h equals 2 row blank blank blank row 6 equals cell negative 3 minus 12 h minus 4 k end cell row 6 equals cell negative 3 minus 12 left parenthesis 2 right parenthesis minus 4 k end cell row 6 equals cell negative 27 minus 4 k end cell row cell 4 k end cell equals cell negative 27 minus 6 end cell row cell 4 k end cell equals cell negative 33 end cell row k equals cell negative 33 over 4 end cell end table

Jadi, nilai h dan k saat 2 p with rightwards arrow on top equals 3 q with rightwards arrow on top minus 4 r with rightwards arrow on top adalah h equals 2 dan k equals negative 33 over 4 

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