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Diketahui dan .Makavektor proyeksi ortogonal dari vektor a pada vektor b adalah ....

Diketahui begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row cell negative sign 4 end cell row cell negative sign 3 end cell row 5 end table close parentheses end style dan begin mathsize 14px style b with rightwards arrow on top equals open parentheses table row cell negative sign 3 end cell row 3 row cell negative sign 1 end cell end table close parentheses end style. Maka vektor proyeksi ortogonal dari vektor  pada vektor  adalah ....

  1. begin mathsize 14px style open parentheses table row cell negative sign 6 over 19 end cell row cell 2 over 19 end cell row cell negative sign 2 over 19 end cell end table close parentheses end style

  2. begin mathsize 14px style open parentheses table row cell 6 over 19 end cell row cell negative sign 2 over 19 end cell row cell 2 over 19 end cell end table close parentheses end style

  3. begin mathsize 14px style open parentheses table row cell negative sign 6 over 19 end cell row cell 6 over 19 end cell row cell negative sign 2 over 19 end cell end table close parentheses end style

  4. begin mathsize 14px style open parentheses table row cell 6 over 19 end cell row cell negative sign 6 over 19 end cell row cell 2 over 19 end cell end table close parentheses end style

  5. begin mathsize 14px style open parentheses table row cell negative sign 6 over 19 end cell row cell 6 over 19 end cell row cell 2 over 19 end cell end table close parentheses end style

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

jawaban yang tepat adalah D.

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Pembahasan

Misalkan vektor proyeksi ortogonal dari vektor terhadap vektor adalah .Oleh karena itu, didapatkan bahwa Jadi, jawaban yang tepat adalah D.

Misalkan vektor proyeksi ortogonal dari vektor begin mathsize 14px style a with rightwards arrow on top end style terhadap vektor begin mathsize 14px style b with rightwards arrow on top end style adalah begin mathsize 14px style p with rightwards arrow on top end style. Oleh karena itu, didapatkan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p with rightwards arrow on top end cell equals cell open parentheses fraction numerator a with rightwards arrow on top ⋅ b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar squared end fraction close parentheses b with rightwards arrow on top end cell row blank equals cell open parentheses fraction numerator open parentheses table row cell negative sign 4 end cell row cell negative sign 3 end cell row 5 end table close parentheses ⋅ open parentheses table row cell negative sign 3 end cell row 3 row cell negative sign 1 end cell end table close parentheses over denominator open parentheses square root of open parentheses negative sign 3 close parentheses squared plus 3 squared plus open parentheses negative sign 1 close parentheses squared end root close parentheses squared end fraction close parentheses open parentheses table row cell negative sign 3 end cell row 3 row cell negative sign 1 end cell end table close parentheses end cell row blank equals cell open parentheses fraction numerator open parentheses negative sign 4 close parentheses ⋅ open parentheses negative sign 3 close parentheses plus open parentheses negative sign 3 close parentheses ⋅ 3 plus 5 ⋅ open parentheses negative sign 1 close parentheses over denominator open parentheses square root of 9 plus 9 plus 1 end root close parentheses squared end fraction close parentheses open parentheses table row cell negative sign 3 end cell row 3 row cell negative sign 1 end cell end table close parentheses end cell row blank equals cell open parentheses fraction numerator 12 minus sign 9 minus sign 5 over denominator open parentheses square root of 19 close parentheses squared end fraction close parentheses open parentheses table row cell negative sign 3 end cell row 3 row cell negative sign 1 end cell end table close parentheses end cell row blank equals cell fraction numerator negative sign 2 over denominator 19 end fraction open parentheses table row cell negative sign 3 end cell row 3 row cell negative sign 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 6 over 19 end cell row cell negative sign 6 over 19 end cell row cell 2 over 19 end cell end table close parentheses end cell end table end style   
 

Jadi, jawaban yang tepat adalah D.

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