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Diketahui vektor, . Proyeksi ortogonal vektor, pada vektor, adalah ...

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PERTANYAAN :

Diketahui vektor straight a with rightwards arrow on top equals open square brackets table row cell negative 4 end cell row 6 end table close square brackets space dan space straight b with rightwards arrow on top equals open square brackets table row 2 row cell negative 1 end cell end table close square brackets. Proyeksi ortogonal vektor straight a with rightwards arrow on top pada vektor b with rightwards arrow on top adalah …

Jawaban

 Proyeksi ortogonal vektor straight a with rightwards arrow on top pada vektor b with rightwards arrow on top adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 14 over denominator 5 end fraction open square brackets table row 2 row cell negative 1 end cell end table close square brackets end cell end table.


Diketahui :

straight a with rightwards arrow on top equals open square brackets table row cell negative 4 end cell row 6 end table close square brackets space dan space straight b with rightwards arrow on top equals open square brackets table row 2 row cell negative 1 end cell end table close square brackets

Ditanya :

Proyeksi ortogonal vektor straight a with rightwards arrow on top pada vektor b with rightwards arrow on top 

Penyelesaian:
Perhatikan perhitungan berikut ini.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight b with rightwards arrow on top close vertical bar squared space end cell equals cell open parentheses square root of 2 squared plus 1 squared end root close parentheses squared end cell row blank equals cell 4 plus 1 end cell row blank equals 5 end table

Proyeksi ortogonal vektor table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight a with rightwards arrow on top end cell end table pada vektor table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight b with rightwards arrow on top end cell end table dapat diperoleh dengan perhitungan berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top space pada space straight b with rightwards arrow on top space end cell equals cell fraction numerator straight a with rightwards arrow on top space straight b with rightwards arrow on top over denominator open vertical bar straight b with rightwards arrow on top close vertical bar squared end fraction straight b with rightwards arrow on top end cell row cell open vertical bar straight b with rightwards arrow on top close vertical bar space end cell equals cell 2 squared plus 1 squared end cell row blank equals cell 4 plus 1 end cell row blank equals 5 row cell straight a with rightwards arrow on top space pada space straight b with rightwards arrow on top end cell equals cell fraction numerator open square brackets table row cell negative 4 end cell row 6 end table close square brackets open square brackets table row 2 row cell negative 1 end cell end table close square brackets over denominator 5 end fraction straight b with rightwards arrow on top end cell row cell straight a with rightwards arrow on top space pada space straight b with rightwards arrow on top end cell equals cell fraction numerator negative 8 minus 6 over denominator 5 end fraction straight b with rightwards arrow on top end cell row cell straight a with rightwards arrow on top space pada space straight b with rightwards arrow on top end cell equals cell fraction numerator negative 14 over denominator 5 end fraction straight b with rightwards arrow on top end cell row cell straight a with rightwards arrow on top space pada space straight b with rightwards arrow on top end cell equals cell fraction numerator negative 14 over denominator 5 end fraction open square brackets table row 2 row cell negative 1 end cell end table close square brackets end cell row blank blank blank end table

Jadi, Proyeksi ortogonal vektor straight a with rightwards arrow on top pada vektor b with rightwards arrow on top adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 14 over denominator 5 end fraction open square brackets table row 2 row cell negative 1 end cell end table close square brackets end cell end table.


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