Diketahui titik A(2, 7, 8), B(−1, 1, −1), dan C(0, 3, 2). AB adalah vektor u dan BC adalah vektor v. Proyeksi vektor ortogonal dari u pada v adalah ....

Pertanyaan

Diketahui titik straight A open parentheses 2 comma space 7 comma space 8 close parenthesesstraight B open parentheses negative 1 comma space 1 comma space minus 1 close parentheses, dan straight C open parentheses 0 comma space 3 comma space 2 close parentheses. AB with rightwards arrow on top adalah vektor u with rightwards arrow on top dan BC with rightwards arrow on top adalah vektor v with rightwards arrow on top. Proyeksi vektor ortogonal dari u with rightwards arrow on top pada v with rightwards arrow on top adalah ....

  1. negative 3 i with hat on top minus 6 j with hat on top minus 9 k with hat on top

  2. i with hat on top plus 2 j with hat on top plus 3 k with hat on top

  3. 1 third i with hat on top plus 2 over 3 j with hat on top plus k with hat on top

  4. negative 9 i with hat on top minus 18 j with hat on top minus 27 k with hat on top

  5. 3 i with hat on top plus 6 j with hat on top plus 9 k with hat on top

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah A.

Diketahui titik straight A open parentheses 2 comma space 7 comma space 8 close parenthesesstraight B open parentheses negative 1 comma space 1 comma space minus 1 close parentheses, dan straight C open parentheses 0 comma space 3 comma space 2 close parentheses, dimana AB with rightwards arrow on top adalah vektor u with rightwards arrow on top dan BC with rightwards arrow on top adalah vektor v with rightwards arrow on top, maka

u with rightwards arrow on top equals straight B minus straight A equals open parentheses table row cell negative 1 end cell row 1 row cell negative 1 end cell end table close parentheses minus open parentheses table row 2 row 7 row 8 end table close parentheses equals open parentheses table row cell negative 3 end cell row cell negative 6 end cell row cell negative 9 end cell end table close parentheses v with rightwards arrow on top equals straight C minus straight B equals open parentheses table row 0 row 3 row 2 end table close parentheses minus open parentheses table row cell negative 1 end cell row 1 row cell negative 1 end cell end table close parentheses equals open parentheses table row 1 row 2 row 3 end table close parentheses

Proyeksi vektor ortogonal dari u with rightwards arrow on top pada v with rightwards arrow on top adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell p with rightwards arrow on top end cell equals cell fraction numerator u with rightwards arrow on top times v with rightwards arrow on top over denominator open vertical bar v with rightwards arrow on top close vertical bar squared end fraction times v with rightwards arrow on top end cell row blank equals cell fraction numerator open parentheses table row cell negative 3 end cell row cell negative 6 end cell row cell negative 9 end cell end table close parentheses times open parentheses table row 1 row 2 row 3 end table close parentheses over denominator 1 squared plus 2 squared plus 3 squared end fraction times open parentheses table row 1 row 2 row 3 end table close parentheses end cell row blank equals cell fraction numerator negative 3 minus 12 minus 27 over denominator 14 end fraction times open parentheses table row 1 row 2 row 3 end table close parentheses end cell row blank equals cell fraction numerator negative 42 over denominator 14 end fraction times open parentheses table row 1 row 2 row 3 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 end cell row cell negative 6 end cell row cell negative 9 end cell end table close parentheses end cell end table

Jadi, proyeksi vektor ortogonal dari u with rightwards arrow on top pada v with rightwards arrow on top adalah negative 3 i with hat on top minus 6 j with hat on top minus 9 k with hat on top

Oleh karena itu, jawaban yang benar adalah A.

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