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Diketahui titik P ( 1 , 0 , 0 ) , Q ( 2 , 1 , 3 ) dan R ( − 1 , 4 , 5 ) . Proyeksi vektor orthogonal QR ⇀ ​ pada QP ⇀ ​ adalah ...

Diketahui titik . Proyeksi vektor orthogonal adalah ...

 

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A. Acfreelance

Master Teacher

Mahasiswa/Alumni UIN Walisongo Semarang

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Proyeksi vektor orthogonal maka

table attributes columnalign right center left columnspacing 0px end attributes row cell QR with rightwards harpoon with barb upwards on top end cell equals cell open parentheses negative 1 comma 4 comma 5 close parentheses minus open parentheses 2 comma 1 comma 3 close parentheses end cell row blank equals cell open parentheses negative 3 comma 3 comma 2 close parentheses end cell row cell open vertical bar stack Q R with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of open parentheses negative 3 close parentheses squared plus open parentheses 3 close parentheses squared plus open parentheses 2 close parentheses squared end root end cell row blank equals cell square root of 9 plus 9 plus 4 end root end cell row blank equals cell square root of 22 end cell row cell stack Q P with rightwards harpoon with barb upwards on top end cell equals cell left parenthesis 1 comma 0 comma 0 right parenthesis minus left parenthesis 2 comma 1 comma 3 right parenthesis end cell row blank equals cell left parenthesis negative 1 comma negative 1 comma negative 3 right parenthesis end cell row cell open vertical bar stack Q P with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of open parentheses negative 1 close parentheses squared plus open parentheses negative 1 close parentheses squared plus open parentheses negative 3 close parentheses squared end root end cell row blank equals cell square root of 11 end cell end table

Proyeksi vektor orthogonal QR with rightwards harpoon with barb upwards on top space pada space QP with rightwards harpoon with barb upwards on top maka

table attributes columnalign right center left columnspacing 0px end attributes row cell vektor space orthogonal space end cell equals cell fraction numerator open parentheses QP with rightwards harpoon with barb upwards on top cross times QR with rightwards harpoon with barb upwards on top close parentheses over denominator open vertical bar QP with rightwards harpoon with barb upwards on top close vertical bar squared end fraction cross times QP end cell row blank equals cell fraction numerator open parentheses open parentheses negative 1 cross times negative 3 close parentheses plus open parentheses negative 1 cross times 3 close parentheses plus open parentheses negative 3 cross times 2 close parentheses close parentheses over denominator open vertical bar square root of 11 close vertical bar squared end fraction cross times open parentheses table row cell negative 1 end cell row cell negative 1 end cell row cell negative 3 end cell end table close parentheses end cell row blank equals cell fraction numerator 3 plus left parenthesis negative 3 right parenthesis plus left parenthesis negative 6 right parenthesis over denominator 11 end fraction open parentheses table row cell negative 1 end cell row cell negative 1 end cell row cell negative 3 end cell end table close parentheses end cell row blank equals cell fraction numerator negative 6 over denominator 11 end fraction open parentheses table row cell negative 1 end cell row cell negative 1 end cell row cell negative 3 end cell end table close parentheses end cell end table

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