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Pertanyaan

Segitiga ABC mempunyai titik-titik sudut straight A open parentheses 2 comma space 3 comma space minus 1 close parentheses comma space straight B open parentheses 3 comma space minus 2 comma space 1 close parentheses dan straight C open parentheses 10 comma space 3 comma space 5 close parentheses, jika stack A B with rightwards arrow on top equals u with rightwards arrow on top dan stack A C with rightwards arrow on top equals v with rightwards arrow on top, maka proyeksi vektor orthogonal vektor u with rightwards arrow on top terhadap v with rightwards arrow on top adalah ...

M. Muhlis

Master Teacher

Mahasiswa/Alumni UIN Maulana Malik Ibrahim Malang

Jawaban terverifikasi

Jawaban

 proyeksi vektor orthogonal vektor u with rightwards arrow on top terhadap v with rightwards arrow on top adalah open parentheses 8 over 5 comma space 0 comma space 6 over 5 close parentheses

Pembahasan

Diketahui straight A open parentheses 2 comma space 3 comma space minus 1 close parentheses comma space straight B open parentheses 3 comma space minus 2 comma space 1 close parentheses dan straight C open parentheses 10 comma space 3 comma space 5 close parentheses,  stack A B with rightwards arrow on top equals u with rightwards arrow on top dan stack A C with rightwards arrow on top equals v with rightwards arrow on top, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top end cell equals cell stack A B with rightwards arrow on top end cell row blank equals cell stack O B with rightwards arrow on top minus stack O A with rightwards arrow on top end cell row blank equals cell open parentheses 3 comma space minus 2 comma space 1 close parentheses minus open parentheses 2 comma space 3 comma space minus 1 close parentheses end cell row blank equals cell open parentheses 1 comma space minus 5 comma space space 2 close parentheses end cell row blank blank blank row cell v with rightwards arrow on top end cell equals cell stack A C with rightwards arrow on top end cell row blank equals cell stack O C with rightwards arrow on top minus stack O A with rightwards arrow on top end cell row blank equals cell open parentheses 10 comma space 3 comma space 5 close parentheses minus open parentheses 2 comma space 3 comma space minus 1 close parentheses end cell row blank equals cell open parentheses 8 comma space 0 comma space 6 close parentheses end cell end table 

Sehinga 

table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top times v with rightwards arrow on top end cell equals cell open parentheses 1 comma space minus 5 comma space 2 close parentheses times open parentheses 8 comma space 0 comma space 6 close parentheses end cell row blank equals cell 8 plus 0 plus 12 end cell row blank equals 20 row blank blank blank row cell open vertical bar v with rightwards arrow on top close vertical bar end cell equals cell square root of 8 squared plus 0 squared plus 6 squared end root end cell row blank equals cell square root of 64 plus 0 plus 36 end root end cell row blank equals cell square root of 100 end cell row blank equals 10 end table 

Maka, proyeksi vektor orthogonal vektor u with rightwards arrow on top terhadap v with rightwards arrow on top adalah 

table attributes columnalign right center left columnspacing 0px end attributes row cell c 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 20 over open parentheses 10 close parentheses squared times open parentheses 8 comma space 0 comma space 6 close parentheses end cell row blank equals cell 20 over 100 times open parentheses 8 comma space 0 comma space 6 close parentheses end cell row blank equals cell 1 fifth times open parentheses 8 comma space 0 comma space 6 close parentheses end cell row blank equals cell open parentheses 8 over 5 comma space 0 comma space 6 over 5 close parentheses end cell end table 

Dengan demikian, proyeksi vektor orthogonal vektor u with rightwards arrow on top terhadap v with rightwards arrow on top adalah open parentheses 8 over 5 comma space 0 comma space 6 over 5 close parentheses

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