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Diketahui proyeksi skalar ortogonal   pada   adala...

Diketahui proyeksi skalar ortogonal a with rightwards arrow on top equals open parentheses table row 3 row cell negative 4 end cell end table close parentheses  pada b with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row p end table close parentheses  adalahnegative 2 square root of 5 Tentukan:

b. proyeksi skalar orthogonal  b with rightwards arrow on top pada a with rightwards arrow on top

Jawaban:

Pertama kita menentukan nilai p, kita dapat menggunakan rumus proyeksi skala orthogonal vektor a with rightwards arrow on top pada b with rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell fraction numerator a with rightwards arrow on top b with rightwards arrow on top over denominator b with rightwards arrow on top end fraction end cell row cell negative 2 square root of 5 end cell equals cell fraction numerator 3 open parentheses negative 2 close parentheses plus open parentheses negative 4 close parentheses open parentheses p close parentheses over denominator square root of open parentheses negative 2 close parentheses squared plus p squared end root end fraction end cell row cell negative 2 square root of 5 end cell equals cell fraction numerator negative 6 minus 4 p over denominator square root of 4 plus p squared end root end fraction end cell row cell square root of open parentheses 4 plus p squared close parentheses 5 end root end cell equals cell fraction numerator negative 6 minus 4 p over denominator negative 2 end fraction end cell row cell square root of 20 plus 5 p squared end root end cell equals cell 3 plus 2 p end cell row cell 20 plus 5 p squared end cell equals cell 9 plus 12 p plus 4 p squared end cell row cell 5 p squared minus 4 p squared minus 12 p plus 20 minus 9 end cell equals 0 row cell p squared minus 12 p plus 11 end cell equals 0 row cell open parentheses p minus 1 close parentheses open parentheses p minus 11 close parentheses end cell equals 0 row p equals cell 1 space atau space p equals 11 end cell end table 

  • untuk p equals 1  proyeksi skala orthogonal vektor b with rightwards arrow on top pada a with rightwards arrow on top

b with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 1 end table close parentheses 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell fraction numerator a with rightwards arrow on top b with rightwards arrow on top over denominator a with rightwards arrow on top end fraction end cell row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell fraction numerator 3 open parentheses negative 2 close parentheses plus open parentheses negative 4 close parentheses open parentheses 1 close parentheses over denominator square root of open parentheses 3 close parentheses squared plus open parentheses negative 4 close parentheses squared end root end fraction end cell row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell fraction numerator negative 6 minus 4 over denominator square root of 25 end fraction end cell row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell fraction numerator negative 10 over denominator 5 end fraction end cell row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell negative 2 end cell end table  

  • untuk p equals 11   proyeksi skala orthogonal vektor b with rightwards arrow on top pada a with rightwards arrow on top

b with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 11 end table close parentheses 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell fraction numerator a with rightwards arrow on top b with rightwards arrow on top over denominator a with rightwards arrow on top end fraction end cell row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell fraction numerator 3 open parentheses negative 2 close parentheses plus open parentheses negative 4 close parentheses open parentheses 11 close parentheses over denominator square root of open parentheses 3 close parentheses squared plus open parentheses negative 4 close parentheses squared end root end fraction end cell row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell fraction numerator negative 6 minus 44 over denominator square root of 25 end fraction end cell row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell fraction numerator negative 50 over denominator 5 end fraction end cell row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell negative 10 end cell end table 

Jadi, proyeksi skalar orthogonal  b with rightwards arrow on top pada a with rightwards arrow on top adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 2 end cell end table  dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 10 end cell end table 

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