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Pertanyaan

Diketahui vektor-vektor u = 2 i + 3 j ​ + k , v = 2 i + 4 j ​ + k , dan w = 2 i − 3 j ​ + 4 k . Hasil dari 4 u − ( 3 v − w ) adalah...

Diketahui vektor-vektor , dan . Hasil dari  adalah... 

  1. 12 i with rightwards arrow on top plus 3 j with rightwards arrow on top plus 5 k with rightwards arrow on top 

  2. 12 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus 5 k with rightwards arrow on top 

  3. 4 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus 5 k with rightwards arrow on top 

  4. 4 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus 3 k with rightwards arrow on top 

  5. 4 i with rightwards arrow on top plus 27 j with rightwards arrow on top plus 5 k with rightwards arrow on top 

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L. Indah

Master Teacher

Mahasiswa/Alumni Universitas Siliwangi

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

jawaban yang benar adalah C.

Pembahasan

Diketahui vektor-vektor , , dan . Vektor kolom dari vektor-vektor tersebut sebagai berikut. Kemudian, hasil dari sebagai berikut. Hasil dari adalah atau . Oleh karena itu, jawaban yang benar adalah C.

Diketahui vektor-vektor u with rightwards arrow on top equals 2 i with rightwards arrow on top plus 3 j with rightwards arrow on top plus k with rightwards arrow on topv with rightwards arrow on top equals 2 i with rightwards arrow on top plus 4 j with rightwards arrow on top plus k with rightwards arrow on top, dan w with rightwards arrow on top equals 2 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus 4 k with rightwards arrow on top. Vektor kolom dari vektor-vektor tersebut sebagai berikut.

u with rightwards arrow on top equals open parentheses table row 2 row 3 row 1 end table close parentheses

v with rightwards arrow on top equals open parentheses table row 2 row 4 row 1 end table close parentheses

w with rightwards arrow on top equals open parentheses table row 2 row cell negative 3 end cell row 4 end table close parentheses

Kemudian, hasil dari 4 u with rightwards arrow on top minus open parentheses 3 v with rightwards arrow on top minus w with rightwards arrow on top close parentheses sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 u with rightwards arrow on top minus open parentheses 3 v with rightwards arrow on top minus w with rightwards arrow on top close parentheses end cell equals cell 4 open parentheses table row 2 row 3 row 1 end table close parentheses minus open square brackets 3 open parentheses table row 2 row 4 row 1 end table close parentheses minus open parentheses table row 2 row cell negative 3 end cell row 4 end table close parentheses close square brackets end cell row blank equals cell open parentheses table row cell 4 times 2 end cell row cell 4 times 3 end cell row cell 4 times 1 end cell end table close parentheses minus open square brackets open parentheses table row cell 3 times 2 end cell row cell 3 times 4 end cell row cell 3 times 1 end cell end table close parentheses minus open parentheses table row 2 row cell negative 3 end cell row 4 end table close parentheses close square brackets end cell row blank equals cell open parentheses table row 8 row 12 row 4 end table close parentheses minus open square brackets open parentheses table row 6 row 12 row 3 end table close parentheses minus open parentheses table row 2 row cell negative 3 end cell row 4 end table close parentheses close square brackets end cell row blank equals cell open parentheses table row 8 row 12 row 4 end table close parentheses minus open parentheses table row cell 6 minus 2 end cell row cell 12 minus open parentheses negative 3 close parentheses end cell row cell 3 minus 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 8 row 12 row 4 end table close parentheses minus open parentheses table row 4 row 15 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 8 minus 4 end cell row cell 12 minus 15 end cell row cell 4 minus open parentheses negative 1 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row 4 row cell negative 3 end cell row 5 end table close parentheses end cell end table

Hasil dari 4 u with rightwards arrow on top minus open parentheses 3 v with rightwards arrow on top minus w with rightwards arrow on top close parentheses adalah open parentheses table row 4 row cell negative 3 end cell row 5 end table close parentheses atau 4 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus 5 k with rightwards arrow on top.

Oleh karena itu, jawaban yang benar adalah C.

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