Roboguru

Diketahui p​=3i+2j​−2k; q​=i−4j​+k dan r=13i+4j​−7k. Jika r=mp​+nq​ maka m−n=...

Pertanyaan

Diketahui straight p with rightwards arrow on top equals 3 straight i with rightwards arrow on top plus 2 straight j with rightwards arrow on top minus 2 straight k with rightwards arrow on top; straight q with rightwards arrow on top equals straight i with rightwards arrow on top minus 4 straight j with rightwards arrow on top plus straight k with rightwards arrow on top dan straight r with rightwards arrow on top equals 13 straight i with rightwards arrow on top plus 4 straight j with rightwards arrow on top minus 7 straight k with rightwards arrow on top. Jika straight r with rightwards arrow on top equals straight m straight p with rightwards arrow on top plus straight n straight q with rightwards arrow on top maka straight m minus straight n equals...

  1. 5

  2. 3

  3. 1

  4. negative 3

  5. negative 5

Pembahasan Soal:

Misalkan terdapat vektor straight a with rightwards arrow on top equals open parentheses table row cell straight a subscript 1 end cell row cell straight a subscript 2 end cell row cell straight a subscript 3 end cell end table close parentheses equals straight a subscript 1 straight i with rightwards arrow on top plus straight a subscript 2 straight j with rightwards arrow on top plus straight a subscript 3 straight k with rightwards arrow on top, straight b with rightwards arrow on top equals open parentheses table row cell straight b subscript 1 end cell row cell straight b subscript 2 end cell row cell straight b subscript 3 end cell end table close parentheses equals straight b subscript 1 straight i with rightwards arrow on top plus straight b subscript 2 straight j with rightwards arrow on top plus straight b subscript 3 straight k with rightwards arrow on top dan straight z adalah skalar. maka berlaku:

open parentheses straight i close parentheses space straight a with rightwards arrow on top plus-or-minus straight b with rightwards arrow on top equals open parentheses table row cell straight a subscript 1 plus-or-minus straight b subscript 1 end cell row cell straight a subscript 2 plus-or-minus straight b subscript 2 straight a subscript 3 plus-or-minus straight b subscript 3 end cell end table close parentheses equals open parentheses straight a subscript 1 plus-or-minus straight b subscript 1 close parentheses straight i with rightwards arrow on top plus open parentheses straight a subscript 2 plus-or-minus straight b subscript 2 close parentheses straight j with rightwards arrow on top plus open parentheses straight a subscript 3 plus-or-minus straight b subscript 3 close parentheses straight k with rightwards arrow on top left parenthesis ii right parenthesis space straight z straight a with rightwards arrow on top equals open parentheses table row cell za subscript 1 end cell row cell za subscript 2 end cell row cell za subscript 3 end cell end table close parentheses equals za subscript 1 straight i with rightwards arrow on top plus za subscript 2 straight j with rightwards arrow on top plus za subscript 3 straight k with rightwards arrow on top

Pada soal diketahui straight p with rightwards arrow on top equals 3 straight i with rightwards arrow on top plus 2 straight j with rightwards arrow on top minus 2 straight k with rightwards arrow on top equals open parentheses table row 3 row 2 row cell negative 2 end cell end table close parentheses; straight q with rightwards arrow on top equals straight i with rightwards arrow on top minus 4 straight j with rightwards arrow on top plus straight k with rightwards arrow on top equals open parentheses table row 1 row cell negative 4 end cell row 1 end table close parentheses dan straight r with rightwards arrow on top equals 13 straight i with rightwards arrow on top plus 4 straight j with rightwards arrow on top minus 7 straight k with rightwards arrow on top equals open parentheses table row 13 row 4 row cell negative 7 end cell end table close parentheses. maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight r with rightwards arrow on top end cell equals cell straight m straight p with rightwards arrow on top plus straight n straight q with rightwards arrow on top end cell row cell open parentheses table row 13 row 4 row cell negative 7 end cell end table close parentheses end cell equals cell straight m open parentheses table row 3 row 2 row cell negative 2 end cell end table close parentheses plus straight n open parentheses table row 1 row cell negative 4 end cell row 1 end table close parentheses end cell row cell open parentheses table row 13 row 4 row cell negative 7 end cell end table close parentheses end cell equals cell open parentheses table row cell 3 straight m end cell row cell 2 straight m end cell row cell negative 2 straight m end cell end table close parentheses plus open parentheses table row straight n row cell negative 4 straight n end cell row straight n end table close parentheses end cell row cell open parentheses table row 13 row 4 row cell negative 7 end cell end table close parentheses end cell equals cell open parentheses table row cell 3 straight m plus straight n end cell row cell 2 straight m minus 4 straight n end cell row cell negative 2 straight m plus straight n end cell end table close parentheses end cell end table

Diperoleh SPLDV yaitu:

open curly brackets table attributes columnalign left end attributes row cell 3 straight m plus straight n equals 13 space... left parenthesis straight i right parenthesis end cell row cell 2 straight m minus 4 straight n equals 4 space... left parenthesis ii right parenthesis end cell row cell negative 2 straight m plus straight n equals negative 7 space... left parenthesis iii right parenthesis end cell end table close

Ambil persamaan (ii) dan (iii) sehingga didapat nilai straight n yaitu:

bottom enclose table attributes columnalign right center left columnspacing 2px end attributes row cell 2 straight m minus 4 straight n end cell equals 4 row cell negative 2 straight m plus straight n end cell equals cell negative 7 space plus end cell end table end enclose table attributes columnalign right center left columnspacing 2px end attributes row cell space space space space space space minus 3 straight n end cell equals cell negative 3 end cell row straight n equals 1 end table

Substitusi persamaan nilai straight n ke persamaan (i) sehingga didapat nilai straight m yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 straight m plus straight n end cell equals 13 row cell 3 straight m plus 1 end cell equals 13 row cell 3 straight m end cell equals cell 13 minus 1 end cell row cell 3 straight m end cell equals 12 row straight m equals 4 end table

Dengan demikian, didapat nilai straight n equals 1 dan straight m equals 4, maka pengurangan m dengan n adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight m minus straight n end cell equals cell 4 minus 1 end cell row cell straight m minus straight n end cell equals 3 end table

Oleh karena itu, jawaban yang benar adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. Hajrianti

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 07 Oktober 2021

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