Roboguru

Pertanyaan

Diberikan vektor a with rightwards arrow on top equals 2 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus k with rightwards arrow on top dan b with rightwards arrow on top equals 6 i with rightwards arrow on top plus j with rightwards arrow on top plus 2 k with rightwards arrow on top. Tentukan hasil dari operasi vektor berikut.

a. a with rightwards arrow on top minus 2 b with rightwards arrow on top
b. 3 a with rightwards arrow on top plus b with rightwards arrow on top

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Jawaban

 hasil dari operasi vektor a with rightwards arrow on top minus 2 b with rightwards arrow on top dan 3 a with rightwards arrow on top plus b with rightwards arrow on top berturut-turut adalah adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 10 i with rightwards arrow on top minus 5 j with rightwards arrow on top minus 3 k with rightwards arrow on top end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 12 i with rightwards arrow on top minus 8 j with rightwards arrow on top plus 5 k with rightwards arrow on top end cell end table.

Pembahasan

Diketahui a with rightwards arrow on top equals 2 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus k with rightwards arrow on top dan b with rightwards arrow on top equals 6 i with rightwards arrow on top plus j with rightwards arrow on top plus 2 k with rightwards arrow on top. Dengan menggunakan konsep perkalian vektor dengan skalar didapatkan

a. a with rightwards arrow on top minus 2 b with rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top minus 2 b with rightwards arrow on top end cell equals cell open parentheses 2 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus k with rightwards arrow on top close parentheses minus 2 open parentheses 6 i with rightwards arrow on top plus j with rightwards arrow on top plus 2 k with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses 2 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus k with rightwards arrow on top close parentheses minus open parentheses 12 i with rightwards arrow on top plus 2 j with rightwards arrow on top plus 4 k with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses 2 minus 12 close parentheses i with rightwards arrow on top plus open parentheses negative 3 minus 2 close parentheses j with rightwards arrow on top plus open parentheses 1 minus 4 close parentheses k with rightwards arrow on top end cell row blank equals cell negative 10 i with rightwards arrow on top minus 5 j with rightwards arrow on top minus 3 k with rightwards arrow on top end cell end table

b. 3 a with rightwards arrow on top plus b with rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a with rightwards arrow on top plus b with rightwards arrow on top end cell equals cell 3 open parentheses 2 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus k with rightwards arrow on top close parentheses plus open parentheses 6 i with rightwards arrow on top plus j with rightwards arrow on top plus 2 k with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses 6 i with rightwards arrow on top minus 9 j with rightwards arrow on top plus 3 k with rightwards arrow on top close parentheses plus open parentheses 6 i with rightwards arrow on top plus j with rightwards arrow on top plus 2 k with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses 6 plus 6 close parentheses i with rightwards arrow on top plus open parentheses negative 9 plus 1 close parentheses j with rightwards arrow on top plus open parentheses 3 plus 2 close parentheses k with rightwards arrow on top end cell row blank equals cell 12 i with rightwards arrow on top minus 8 j with rightwards arrow on top plus 5 k with rightwards arrow on top end cell end table

Dengan demikian, hasil dari operasi vektor a with rightwards arrow on top minus 2 b with rightwards arrow on top dan 3 a with rightwards arrow on top plus b with rightwards arrow on top berturut-turut adalah adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 10 i with rightwards arrow on top minus 5 j with rightwards arrow on top minus 3 k with rightwards arrow on top end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 12 i with rightwards arrow on top minus 8 j with rightwards arrow on top plus 5 k with rightwards arrow on top end cell end table.

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