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Diketahui  dan . Jika c adalah vektor proyeksi ortogonal a terhadap b dan panjang vektor  memiliki panjang yang sama dengan vektor c→, maka nilai dari 5x2​ 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 1 row 4 end table close parentheses end style dan begin mathsize 14px style italic b with rightwards arrow on top equals open parentheses table row 2 row cell negative sign 6 end cell row cell negative sign 9 end cell end table close parentheses end style. Jika c with rightwards arrow on top adalah vektor proyeksi ortogonal italic a with rightwards arrow on top terhadap begin mathsize 14px style italic b with rightwards arrow on top end style dan panjang vektor begin mathsize 14px style italic d with rightwards arrow on top equals open parentheses table row 2 row cell negative sign 1 end cell row italic x end table close parentheses end style memiliki panjang yang sama dengan vektor begin mathsize 14px style italic c with italic rightwards arrow on top end style, maka nilai dari begin mathsize 14px style italic x squared over 5 end style adalah ....

  1. begin mathsize 14px style 379 over 121 end style 

  2. begin mathsize 14px style 379 over 11 end style 

  3. begin mathsize 14px style 397 over 121 end style 

  4. begin mathsize 14px style 397 over 11 end style 

  5. begin mathsize 14px style 399 over 121 end style 

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Karena undefined adalah vektor proyeksi ortogonal begin mathsize 14px style italic a with rightwards arrow on top end style terhadap begin mathsize 14px style italic b with italic rightwards arrow on top end style, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar italic c with rightwards arrow on top close vertical bar end cell equals cell open vertical bar fraction numerator italic a with italic rightwards arrow on top ⋅ italic b with rightwards arrow on top over denominator open vertical bar italic 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 1 row 4 end table close parentheses ⋅ open parentheses table row 2 row cell negative sign 6 end cell row cell negative sign 9 end cell end table close parentheses over denominator square root of 2 squared plus open parentheses negative sign 6 close parentheses squared plus open parentheses negative sign 9 close parentheses squared end root end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator negative sign 4 ⋅ 2 plus 1 ⋅ open parentheses negative sign 6 close parentheses plus 4 ⋅ open parentheses negative sign 9 close parentheses over denominator square root of 4 plus 36 plus 81 end root end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator negative sign 8 minus sign 6 minus sign 36 over denominator square root of 121 end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator negative sign 50 over denominator 11 end fraction close vertical bar end cell row blank equals cell 50 over 11 end cell end table

Karena panjang vektor begin mathsize 14px style italic d with italic rightwards arrow on top equals open parentheses table row 2 row cell negative sign 1 end cell row italic x end table close parentheses end style memiliki panjang yang sama dengan vektor begin mathsize 14px style italic c with rightwards arrow on top end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar italic d with rightwards arrow on top close vertical bar end cell equals cell open vertical bar italic c with rightwards arrow on top close vertical bar end cell row cell square root of 2 squared plus open parentheses negative sign 1 close parentheses squared plus italic x squared end root end cell equals cell 50 over 11 end cell row cell square root of 4 plus 1 plus italic x squared end root end cell equals cell 50 over 11 end cell row cell square root of 5 plus italic x squared end root end cell equals cell 50 over 11 end cell row cell 5 plus italic x squared end cell equals cell fraction numerator 2.500 over denominator 121 end fraction end cell row cell italic x squared end cell equals cell fraction numerator 2.500 over denominator 121 end fraction minus sign 5 end cell row cell italic x squared end cell equals cell fraction numerator 2.500 over denominator 121 end fraction minus sign 605 over 121 end cell row cell italic x squared end cell equals cell fraction numerator 1.895 over denominator 121 end fraction end cell row cell italic x squared over 5 end cell equals cell 379 over 121 end cell end table end style  

Jadi, jawaban yang tepat adalah A.

51

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