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Pertanyaan

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 begin mathsize 14px style a with rightwards arrow on top end style pada vektor begin mathsize 14px style b with rightwards arrow on top end style 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

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

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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Diketahui  dan . Jika p→​ adalah vektor proyeksi ortogonal a→ pada b→ dan q​ adalah vektor proyeksi ortogonal b pada a, maka p​⋅q​=....

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