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Diketahui  dan . Maka panjang vektor proyeksi ortogonal dari vektor a terhadap vektor b adalah ....

Pertanyaan

Diketahui begin mathsize 14px style italic 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 italic 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 panjang vektor proyeksi ortogonal dari vektor begin mathsize 14px style italic a with rightwards arrow on top end style terhadap vektor begin mathsize 14px style italic b with rightwards arrow on top end style adalah ....

  1. undefined

  2. undefined

  3. undefined

  4. undefined

  5. undefined

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Misalkan vektor proyeksi ortogonal dari vektor undefined terhadap vektor undefined adalah begin mathsize 14px style italic 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 open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell open vertical bar 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 end fraction close vertical bar end cell row blank equals cell open vertical bar 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 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 end fraction close vertical bar end cell row blank equals cell open vertical bar 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 square root of 9 plus 9 plus 1 end root end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator 12 minus sign 9 minus sign 5 over denominator square root of 19 end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator negative sign 2 over denominator square root of 19 end fraction close vertical bar end cell row blank equals cell fraction numerator 2 over denominator square root of 19 end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 19 end fraction ⋅ fraction numerator square root of 19 over denominator square root of 19 end fraction end cell row blank equals cell fraction numerator 2 square root of 19 over denominator 19 end fraction end cell end table end style   
 

Jadi, jawaban yang tepat adalah E.

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