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

Pertanyaan

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

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

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

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

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

  5. negative 62 i with hat on top minus 23 j with hat on top plus 3 k with hat on top

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah B.

Diketahui bahwa, vektor a with rightwards arrow on top equals 6 x i with hat on top plus 2 x j with hat on top minus 8 k with hat on topb with rightwards arrow on top equals negative 4 i with hat on top plus 8 j with hat on top plus 10 k with hat on top, dan c with rightwards arrow on top equals negative 2 i with hat on top plus 3 j with hat on top minus 5 k with hat on top. vektor a with rightwards arrow on top space dan space b with rightwards arrow on top tegak lurus. Ingat bahwa, dua buah vektor dikatakan tegak lurus jika hasil kali dot productnya adalah nol, maka

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 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 negative 10 end cell end table

vektor open parentheses a with rightwards arrow on top minus c with rightwards arrow on top close parentheses 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 6 open parentheses negative 10 close parentheses end cell row cell 2 open parentheses negative 10 close parentheses end cell row 8 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 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 58 end cell row cell negative 23 end cell row cell negative 3 end cell end table close parentheses end cell end table

Jadi, open parentheses a with rightwards arrow on top minus c with rightwards arrow on top close parentheses equals negative 58 i with hat on top minus 23 j with hat on top minus 3 k with hat on top

Oleh karena itu, jawaban yang benar adalah B.

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