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Pertanyaan

Diketahui vektor OP = ( 3 , − 2 ) , OQ ​ = ( − 1 , 5 ) , OR = ( 7 , 4 ) . Jika vektor a mewakili PQ ​ , vektor b mewakili QR ​ , dan vektor c mewakili PR ,hitunglah 2 b − 3 c + a !

Diketahui vektor . Jika vektor  mewakili , vektor  mewakili , dan vektor  mewakili , hitunglah !

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D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

vektor adalah .

 vektor begin mathsize 14px style 2 b with rightwards arrow on top minus 3 c with rightwards arrow on top plus a with rightwards arrow on top end style adalah begin mathsize 14px style open parentheses table row 0 row cell negative 13 end cell end table close parentheses end style.

Pembahasan

Dengan menerapkan konsep operasi vektor, diperoleh: Jadi,vektor adalah .

Dengan menerapkan konsep operasi vektor, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 b with rightwards arrow on top minus 3 c with rightwards arrow on top plus a with rightwards arrow on top end cell row blank equals cell 2 QR with rightwards arrow on top minus 3 PR with rightwards arrow on top plus PQ with rightwards arrow on top end cell row blank equals cell 2 open parentheses OR with rightwards arrow on top minus OQ with rightwards arrow on top close parentheses minus 3 open parentheses OR with rightwards arrow on top minus OP with rightwards arrow on top close parentheses plus open parentheses OQ with rightwards arrow on top minus OP with rightwards arrow on top close parentheses end cell row blank equals cell 2 OR with rightwards arrow on top minus 2 OQ with rightwards arrow on top minus 3 OR with rightwards arrow on top plus 3 OP with rightwards arrow on top plus OQ with rightwards arrow on top minus OP with rightwards arrow on top end cell row blank equals cell negative OR with rightwards arrow on top minus OQ with rightwards arrow on top plus 2 OP with rightwards arrow on top end cell row blank equals cell negative 1 open parentheses table row 7 row 4 end table close parentheses minus 1 open parentheses table row cell negative 1 end cell row 5 end table close parentheses plus 2 open parentheses table row 3 row cell negative 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 7 end cell row cell negative 4 end cell end table close parentheses minus open parentheses table row cell negative 1 end cell row 5 end table close parentheses plus open parentheses table row 6 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 row cell negative 13 end cell end table close parentheses end cell end table end style 

Jadi, vektor begin mathsize 14px style 2 b with rightwards arrow on top minus 3 c with rightwards arrow on top plus a with rightwards arrow on top end style adalah begin mathsize 14px style open parentheses table row 0 row cell negative 13 end cell end table close parentheses end style.

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Jika p ​ , q ​ , r dan t adalah vektor posisi dari P ( − 1 , 2 , 2 1 ​ ) ; Q ( 3 , 0 , 2 ) ; R ( 2 , 3 , 1 ) dan T ( 9 , − 14 , 2 ) , maka nilai k yang memenuhi k p ​ + 3 q ​ − 2 r = t adalah....

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