Roboguru

Diketahui vektor a=6xi+2xj​−8k, b=−4i+8j​+10k, dan c=−2i+3j​−5k. Jika vektor a tegak lurus b, maka vektor a−c=...

Pertanyaan

Diketahui vektor a with rightwards arrow on top equals 6 x i with rightwards arrow on top plus 2 x j with rightwards arrow on top minus 8 k with rightwards arrow on top, b with rightwards arrow on top equals negative 4 i with rightwards arrow on top plus 8 j with rightwards arrow on top plus 10 k with rightwards arrow on top, dan c with rightwards arrow on top equals negative 2 i with rightwards arrow on top plus 3 j with rightwards arrow on top minus 5 k with rightwards arrow on top. Jika vektor a with rightwards arrow on top tegak lurus b with rightwards arrow on top, maka vektor a with rightwards arrow on top minus c with rightwards arrow on top equals...space 

  1. negative 58 i with rightwards arrow on top minus 20 j with rightwards arrow on top minus 3 k with rightwards arrow on top 

  2. negative 58 i with rightwards arrow on top minus 23 j with rightwards arrow on top minus 3 k with rightwards arrow on top 

  3. negative 62 i with rightwards arrow on top minus 20 j with rightwards arrow on top minus 3 k with rightwards arrow on top 

  4. negative 62 i with rightwards arrow on top minus 23 j with rightwards arrow on top minus 3 k with rightwards arrow on top 

  5. negative 62 i with rightwards arrow on top minus 23 j with rightwards arrow on top minus 3 k with rightwards arrow on top

Pembahasan:

Misalkan a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell row cell a subscript 3 end cell end table close parentheses dan b with rightwards arrow on top equals open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell row cell b subscript 3 end cell end table close parentheses. Jika vektor a with rightwards arrow on top tegak lurus b with rightwards arrow on top, maka berlaku:

a with rightwards arrow on top times b with rightwards arrow on top equals 0 

Dimana:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell row cell a subscript 3 end cell end table close parentheses times open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell row cell b subscript 3 end cell end table close parentheses end cell row blank equals cell a subscript 1 b subscript 1 plus a subscript 2 b subscript 2 plus a subscript 3 b subscript 3 end cell end table 

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell 6 x i with rightwards arrow on top plus 2 x j with rightwards arrow on top minus 8 k with rightwards arrow on top end cell row cell b with rightwards arrow on top end cell equals cell negative 4 i with rightwards arrow on top plus 8 j with rightwards arrow on top plus 10 k with rightwards arrow on top end cell row cell c with rightwards arrow on top end cell equals cell negative 2 i with rightwards arrow on top plus 3 j with rightwards arrow on top minus 5 k with rightwards arrow on top end cell end table 

Tentukan nilai x vektor a with rightwards arrow on top menggunakan rumus dua vektor saling tegak lurus.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals 0 row cell open parentheses table row cell 6 x end cell row cell 2 x end cell row cell negative 8 end cell end table close parentheses times open parentheses table row cell negative 4 end cell row 8 row 10 end table close parentheses end cell equals 0 row cell 6 x times open parentheses negative 4 close parentheses plus 2 x times 8 plus open parentheses negative 8 close parentheses times 10 end cell equals 0 row cell negative 24 x plus 16 x minus 80 end cell equals 0 row cell negative 8 x end cell equals 80 row x equals cell fraction numerator 80 over denominator negative 8 end fraction end cell row x equals cell negative 10 end cell end table 

Sehingga, vektor a with rightwards arrow on top adalah: 

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell open parentheses table row cell 6 x end cell row cell 2 x end cell row cell negative 8 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 6 times open parentheses negative 10 close parentheses end cell row cell 2 times open parentheses negative 10 close parentheses end cell row cell negative 8 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 60 end cell row cell negative 20 end cell row cell negative 8 end cell end table close parentheses end cell end table 

Maka, a with rightwards arrow on top minus c with rightwards arrow on top adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top minus c with rightwards arrow on top end cell equals cell open parentheses table row cell negative 60 end cell row cell negative 20 end cell row cell negative 8 end cell end table close parentheses minus open parentheses table row cell negative 2 end cell row 3 row cell negative 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 60 plus 2 end cell row cell negative 20 minus 3 end cell row cell negative 8 plus 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 58 end cell row cell negative 23 end cell row cell negative 3 end cell end table close parentheses end cell end table 

Sehingga, vektor a with rightwards arrow on top minus c with rightwards arrow on top equals negative 58 i with rightwards arrow on top minus 23 j with rightwards arrow on top minus 3 k with rightwards arrow on top.

Jadi, jawaban yang tepat adalah B.

Jawaban terverifikasi

Dijawab oleh:

A. Acfreelance

Mahasiswa/Alumni Universitas Indraprasta PGRI

Terakhir diupdate 06 Oktober 2021

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