Diketahui koordinat A(−4, 2, 3), B(7, 8, −1), dan C(1, 0, 7). Jika AB wakil dari vektor u, AC wakil dari vektor v, maka proyeksi vektor ortogonal dari u pada v adalah ....

Pertanyaan

Diketahui koordinat straight A open parentheses negative 4 comma space 2 comma space 3 close parenthesesstraight B open parentheses 7 comma space 8 comma space minus 1 close parentheses, dan straight C open parentheses 1 comma space 0 comma space 7 close parentheses. Jika AB with rightwards arrow on top wakil dari vektor u with rightwards arrow on topAC with rightwards arrow on top wakil dari vektor v with rightwards arrow on top, maka proyeksi vektor ortogonal dari u with rightwards arrow on top pada v with rightwards arrow on top adalah ....

  1. 3 i with hat on top minus 6 over 5 j with hat on top plus fraction numerator 12 over denominator square root of 5 end fraction k with hat on top

  2. 3 square root of 5 i with hat on top minus fraction numerator 6 over denominator square root of 5 end fraction j with hat on top plus fraction numerator 12 over denominator square root of 5 end fraction k with hat on top

  3. 9 over 5 open parentheses 5 i with hat on top minus 2 j with hat on top plus 4 k with hat on top close parentheses

  4. 3 over 5 open parentheses 5 i with hat on top minus 2 j with hat on top plus 4 k with hat on top close parentheses

  5. 9 over 55 open parentheses 5 i with hat on top minus 2 j with hat on top plus 4 k with hat on top close parentheses

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah D.

Diketahui koordinat straight A open parentheses negative 4 comma space 2 comma space 3 close parenthesesstraight B open parentheses 7 comma space 8 comma space minus 1 close parentheses, dan straight C open parentheses 1 comma space 0 comma space 7 close parentheses, dimana AB with rightwards arrow on top wakil dari vektor u with rightwards arrow on topAC with rightwards arrow on top wakil dari vektor v with rightwards arrow on top, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top end cell equals cell straight B minus straight A end cell row blank equals cell open parentheses table row 7 row 8 row cell negative 1 end cell end table close parentheses minus open parentheses table row cell negative 4 end cell row 2 row 3 end table close parentheses end cell row blank equals cell open parentheses table row 11 row 6 row cell negative 4 end cell end table close parentheses end cell row cell v with rightwards arrow on top end cell equals cell straight C minus straight A end cell row blank equals cell open parentheses table row 1 row 0 row 7 end table close parentheses minus open parentheses table row cell negative 4 end cell row 2 row 3 end table close parentheses end cell row blank equals cell open parentheses table row 5 row cell negative 2 end cell row 4 end table close parentheses end cell end table

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 11 row 6 row cell negative 4 end cell end table close parentheses times open parentheses table row 5 row cell negative 2 end cell row 4 end table close parentheses over denominator 5 squared plus open parentheses negative 2 close parentheses squared plus 4 squared end fraction times open parentheses table row 5 row cell negative 2 end cell row 4 end table close parentheses end cell row blank equals cell fraction numerator 55 minus 12 minus 16 over denominator 25 plus 4 plus 16 end fraction times open parentheses table row 5 row cell negative 2 end cell row 4 end table close parentheses end cell row blank equals cell 27 over 45 times open parentheses table row 5 row cell negative 2 end cell row 4 end table close parentheses end cell row blank equals cell 3 over 5 times open parentheses table row 5 row cell negative 2 end cell row 4 end table close parentheses end cell row blank equals cell 3 over 5 open parentheses 5 i with hat on top minus 2 j with hat on top plus 4 k with hat on top close parentheses end cell end table

Oleh karena itu, jawaban yang benar adalah D.

36

5.0 (2 rating)

Pertanyaan serupa

Diketahui segitiga ABC dengan titik A(−2, 3, 1), B(1, −1, 0), dan C(−1, 1, 0). Proyeksi vektor ortogonal dari AB terhadap AC adalah ....

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Jawaban terverifikasi

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