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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 ....

Pertanyaan

Diketahui segitiga ABC dengan titik straight A open parentheses negative 2 comma space 3 comma space 1 close parenthesesstraight B open parentheses 1 comma space minus 1 comma space 0 close parentheses, dan straight C open parentheses negative 1 comma space 1 comma space 0 close parentheses. Proyeksi vektor ortogonal dari AB with rightwards arrow on top terhadap AC with rightwards arrow on top adalah ....

  1. 2 i with hat on top minus 4 j with hat on top plus 2 k with hat on top

  2. 2 i with hat on top minus 4 j with hat on top minus 2 k with hat on top

  3. 2 i with hat on top plus 4 j with hat on top minus 2 k with hat on top

  4. i with hat on top minus 2 j with hat on top minus k with hat on top

  5. i with hat on top plus 2 j with hat on top minus k with hat on top

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah B.

Diketahui segitiga ABC dengan titik straight A open parentheses negative 2 comma space 3 comma space 1 close parenthesesstraight B open parentheses 1 comma space minus 1 comma space 0 close parentheses, dan straight C open parentheses negative 1 comma space 1 comma space 0 close parentheses, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell straight B minus straight A end cell row blank equals cell open parentheses table row 1 row cell negative 1 end cell row 0 end table close parentheses minus open parentheses table row cell negative 2 end cell row 3 row 1 end table close parentheses end cell row blank equals cell open parentheses table row 3 row cell negative 4 end cell row cell negative 1 end cell end table close parentheses end cell row cell AC with rightwards arrow on top end cell equals cell straight C minus straight A end cell row blank equals cell open parentheses table row cell negative 1 end cell row 1 row 0 end table close parentheses minus open parentheses table row cell negative 2 end cell row 3 row 1 end table close parentheses end cell row blank equals cell open parentheses table row 1 row cell negative 2 end cell row cell negative 1 end cell end table close parentheses end cell end table

Proyeksi vektor ortogonal dari AB with rightwards arrow on top terhadap AC with rightwards arrow on top 

table attributes columnalign right center left columnspacing 0px end attributes row cell p with rightwards arrow on top end cell equals cell fraction numerator stack A B with rightwards arrow on top times stack A C with rightwards arrow on top over denominator open vertical bar stack A C with rightwards arrow on top close vertical bar squared end fraction times stack A C with rightwards arrow on top end cell row blank equals cell fraction numerator open parentheses table row 3 row cell negative 4 end cell row cell negative 1 end cell end table close parentheses times open parentheses table row 1 row cell negative 2 end cell row cell negative 1 end cell end table close parentheses over denominator 1 squared plus open parentheses negative 2 close parentheses squared plus open parentheses negative 1 close parentheses squared end fraction times open parentheses table row 1 row cell negative 2 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell fraction numerator 3 plus 8 plus 1 over denominator 1 plus 4 plus 1 end fraction times open parentheses table row 1 row cell negative 2 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell 12 over 6 times open parentheses table row 1 row cell negative 2 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell negative 4 end cell row cell negative 2 end cell end table close parentheses end cell row blank equals cell 2 i with hat on top minus 4 j with hat on top minus 2 k with hat on top end cell end table

Oleh karena itu, jawaban yang benar adalah B.

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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 ....

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Jawaban terverifikasi

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