Roboguru

Diketahui a=−i+j​−k, b=i−2j​+k, c=−4i+xk dan a⋅(b+c)=a⋅a. Tentukan nilai x!

Pertanyaan

Diketahui a with rightwards arrow on top equals negative i with rightwards arrow on top plus j with rightwards arrow on top minus k with rightwards arrow on topb with rightwards arrow on top equals i with rightwards arrow on top minus 2 j with rightwards arrow on top plus k with rightwards arrow on topc with rightwards arrow on top equals negative 4 i with rightwards arrow on top plus x k with rightwards arrow on top dan a with rightwards arrow on top times open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses equals a with rightwards arrow on top times a with rightwards arrow on top. Tentukan nilai x!

Pembahasan:

Diberikan vektor a with rightwards arrow on top equals negative i with rightwards arrow on top plus j with rightwards arrow on top minus k with rightwards arrow on top,  b with rightwards arrow on top equals i with rightwards arrow on top minus 2 j with rightwards arrow on top plus k with rightwards arrow on topc with rightwards arrow on top equals negative 4 i with rightwards arrow on top plus x k with rightwards arrow on top dan persamaan a with rightwards arrow on top times open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses equals a with rightwards arrow on top times a with rightwards arrow on top.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses end cell equals cell a with rightwards arrow on top times a with rightwards arrow on top end cell row cell open parentheses table row 1 row 1 row cell negative 1 end cell end table close parentheses times open parentheses open parentheses table row 1 row cell negative 2 end cell row 1 end table close parentheses plus open parentheses table row cell negative 4 end cell row 0 row x end table close parentheses close parentheses end cell equals cell open parentheses table row 1 row 1 row cell negative 1 end cell end table close parentheses times open parentheses table row 1 row 1 row cell negative 1 end cell end table close parentheses end cell row cell open parentheses table row 1 row 1 row cell negative 1 end cell end table close parentheses times open parentheses table row cell negative 3 end cell row cell negative 2 end cell row cell 1 plus x end cell end table close parentheses end cell equals cell open parentheses table row 1 row 1 row cell negative 1 end cell end table close parentheses times open parentheses table row 1 row 1 row cell negative 1 end cell end table close parentheses end cell row cell negative 3 minus 2 minus left parenthesis 1 plus x right parenthesis end cell equals cell 1 plus 1 plus 1 end cell row cell negative 5 minus 1 minus x end cell equals 3 row cell negative 6 minus x end cell equals 3 row cell negative x end cell equals cell 3 plus 6 end cell row cell negative x end cell equals 9 row x equals cell negative 9 end cell end table 

Jadi, nilai x adalah negative 9.

Jawaban terverifikasi

Dijawab oleh:

I. Kumaralalita

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 06 Oktober 2021

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Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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