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Diketahui  dan . Proyeksi skalar a→ pada b adalah 4 dan ∣b→∣=9. Jika y>0, maka nilai dari ∣∣​a∣∣​ adalah ....

Pertanyaan

Diketahui begin mathsize 14px style italic a with rightwards arrow on top equals open parentheses table row cell negative sign 8 end cell row italic x row 4 end table close parentheses end style dan begin mathsize 14px style italic b with italic rightwards arrow on top equals open parentheses table row 1 row cell negative sign 4 end cell row italic y end table close parentheses end style. Proyeksi skalar italic a with italic rightwards arrow on top pada begin mathsize 14px style italic b with rightwards arrow on top end style adalah 4 dan begin mathsize 14px style vertical line b with italic rightwards arrow on top vertical line equals 9 end style. Jika begin mathsize 14px style italic y greater than 0 end style, maka nilai dari begin mathsize 14px style open vertical bar italic a with rightwards arrow on top close vertical bar end style adalah ....

  1. begin mathsize 14px style square root of 79 end style 

  2. begin mathsize 14px style square root of 89 end style 

  3. begin mathsize 14px style square root of 98 end style 

  4. begin mathsize 14px style square root of 105 end style 

  5. begin mathsize 14px style square root of 114 end style 

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Karena begin mathsize 14px style open vertical bar italic b with rightwards arrow on top close vertical bar equals 9 end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar italic b with italic rightwards arrow on top close vertical bar end cell equals 9 row cell square root of 1 squared plus open parentheses negative sign 4 close parentheses squared plus italic y squared end root end cell equals 9 row cell square root of 1 plus 16 plus italic y squared end root end cell equals 9 row cell 1 plus 16 plus italic y squared end cell equals 81 row cell 17 plus italic y squared end cell equals 81 row cell italic y squared end cell equals 64 row italic y equals cell plus-or-minus 8 end cell end table end style 

Karena undefined, maka begin mathsize 14px style italic y equals 8 end style 

Oleh karena itu,

begin mathsize 14px style italic b with italic rightwards arrow on top equals open parentheses table row 1 row cell negative sign 4 end cell row italic y end table close parentheses equals open parentheses table row 1 row cell negative sign 4 end cell row 8 end table close parentheses end style 

Karena proyeksi skalar italic a with rightwards arrow on top pada begin mathsize 14px style italic b with italic rightwards arrow on top end style adalah 3, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 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 end cell equals 4 row cell fraction numerator open parentheses table row cell negative sign 8 end cell row italic x row 4 end table close parentheses ⋅ open parentheses table row 1 row cell negative sign 4 end cell row 8 end table close parentheses over denominator 9 end fraction end cell equals 4 row cell fraction numerator negative sign 8 ⋅ 1 plus italic x ⋅ open parentheses negative sign 4 close parentheses plus 4 ⋅ 8 over denominator 9 end fraction end cell equals 4 row cell fraction numerator negative sign 8 minus sign 4 italic x plus 32 over denominator 9 end fraction end cell equals 4 row cell fraction numerator negative sign 4 italic x plus 24 over denominator 9 end fraction end cell equals 4 row cell negative sign 4 italic x plus 24 end cell equals 36 row cell negative sign 4 italic x end cell equals 12 row italic x equals cell negative sign 3 end cell end table end style 

Oleh karena itu,

begin mathsize 14px style italic a with italic rightwards arrow on top equals open parentheses table row cell negative sign 8 end cell row italic x row 4 end table close parentheses equals open parentheses table row cell negative sign 8 end cell row cell negative sign 3 end cell row 4 end table close parentheses end style 

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar italic a with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative sign 8 close parentheses squared plus open parentheses negative sign 3 close parentheses squared plus 4 squared end root end cell row blank equals cell square root of 64 plus 9 plus 16 end root end cell row blank equals cell square root of 64 plus 9 plus 16 end root end cell row blank equals cell square root of 89 end cell end table 

Jadi, jawaban yang tepat adalah B.

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