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Diketahui a=3i−2j​, b=−i+4j​, dan r=7i−8j​. Jika r=ka+mb, maka k+m=....

Pertanyaan

Diketahui a with rightwards arrow on top equals 3 i with hat on top minus 2 j with hat on top comma space b with rightwards arrow on top equals negative i with hat on top plus 4 j with hat on top, dan r with rightwards arrow on top equals 7 i with hat on top minus 8 j with hat on top. Jika r with rightwards arrow on top equals k a with rightwards arrow on top plus m b with rightwards arrow on top, maka k plus m equals....

  1. 3

  2. 2

  3. 1

  4. negative 1

  5. negative 2

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah C.

Diketahui a with rightwards arrow on top equals 3 i with hat on top minus 2 j with hat on top comma space b with rightwards arrow on top equals negative i with hat on top plus 4 j with hat on top, dan r with rightwards arrow on top equals 7 i with hat on top minus 8 j with hat on top. Jika r with rightwards arrow on top equals k a with rightwards arrow on top plus m b with rightwards arrow on top, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell r with rightwards arrow on top end cell equals cell k open parentheses 3 i with hat on top minus 2 j with hat on top close parentheses plus m open parentheses negative i with hat on top plus 4 j with hat on top close parentheses end cell row cell 7 i with hat on top minus 8 j with hat on top end cell equals cell open parentheses 3 k minus m close parentheses i with hat on top plus open parentheses negative 2 k plus 4 m close parentheses j with hat on top end cell row 7 equals cell 3 k minus m..... left parenthesis 1 end cell row cell negative 8 end cell equals cell negative 2 k plus 4 m..... left parenthesis 2 end cell end table

Dengan mengalikan persamaan (1 dengan 4, maka didapatkan

table attributes columnalign right center left columnspacing 0px end attributes row cell 12 k minus 4 m end cell equals 28 row cell 4 m end cell equals cell 12 k minus 28..... left parenthesis 3 end cell end table

substitusikan persamaan (3 pada persamaan (2 sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 8 end cell equals cell negative 2 k plus 12 k minus 28 end cell row 20 equals cell 10 k end cell row k equals 2 row cell 4 m end cell equals cell 12 open parentheses 2 close parentheses minus 28 end cell row blank equals cell 24 minus 28 end cell row blank equals cell negative 4 end cell row m equals cell negative 1 end cell end table

Jadi, k plus m equals 1

Oleh karena itu, jawaban yang benar adalah C.

237

4.8 (15 rating)

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