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Diketahui  dan . Proyeksi skalar a pada b adalah 6 dan ∣∣​a∣∣​=181​. Nilai yang mungkin dari x−y adalah ....

Pertanyaan

Diketahui undefined dan begin mathsize 14px style italic b with rightwards arrow on top equals open parentheses table row cell negative sign 2 end cell row 3 row cell negative sign 6 end cell end table close parentheses end style. Proyeksi skalar begin mathsize 14px style italic a with rightwards arrow on top end style pada begin mathsize 14px style italic b with rightwards arrow on top end style adalah 6 dan open vertical bar italic a with rightwards arrow on top close vertical bar equals square root of 181. Nilai yang mungkin dari undefined adalah ....

  1. begin mathsize 14px style negative sign 17 end style 

  2. begin mathsize 14px style negative sign 8 end style 

  3. 11

  4. 12

  5. 13

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Karena proyeksi skalar italic a with rightwards arrow on top pada italic b with rightwards arrow on top adalah 6, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator italic a with rightwards arrow on top ⋅ italic b with italic rightwards arrow on top over denominator italic b with rightwards arrow on top end fraction end cell equals 6 row cell fraction numerator open parentheses table row cell negative sign 6 end cell row italic x row italic y end table close parentheses ⋅ open parentheses table row cell negative sign 2 end cell row 3 row cell negative sign 6 end cell end table close parentheses over denominator square root of open parentheses negative sign 2 close parentheses squared plus 3 squared plus open parentheses negative sign 6 close parentheses squared end root end fraction end cell equals 6 row cell fraction numerator negative sign 6 ⋅ open parentheses negative sign 2 close parentheses plus italic x ⋅ 3 plus italic y ⋅ open parentheses negative sign 6 close parentheses over denominator square root of 4 plus 9 plus 36 end root end fraction end cell equals 6 row cell fraction numerator 12 plus 3 italic x minus sign 6 italic y over denominator square root of 49 end fraction end cell equals 6 row cell fraction numerator 12 plus 3 italic x minus sign 6 italic y over denominator 7 end fraction end cell equals 6 row cell 12 plus 3 italic x minus sign 6 italic y end cell equals 42 row cell 3 italic x minus sign 6 italic y end cell equals 30 row cell italic x minus sign 2 italic y end cell equals 10 row italic x equals cell 10 plus 2 italic y end cell end table end style

Karena begin mathsize 14px style open vertical bar italic a with rightwards arrow on top close vertical bar equals square root of 181 end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar italic a with text ⃗ end text on top close vertical bar end cell equals cell square root of 181 end cell row cell square root of open parentheses negative sign 6 close parentheses squared plus italic x squared plus italic y squared end root end cell equals cell square root of 181 end cell row cell square root of 36 plus italic x squared plus italic y squared end root end cell equals cell square root of 191 end cell row cell 36 plus italic x squared plus italic y squared end cell equals 181 row cell italic x squared plus italic y squared end cell equals 145 row cell open parentheses 10 plus 2 italic y close parentheses squared plus italic y squared end cell equals 145 row cell 100 plus 40 italic y plus 4 italic y squared plus italic y squared end cell equals 145 row cell 5 italic y squared plus 40 italic y plus 100 end cell equals 145 row cell 5 italic y squared plus 40 italic y minus sign 45 end cell equals 0 row cell italic y squared plus 8 italic y minus sign 9 end cell equals 0 row cell open parentheses italic y plus 9 close parentheses open parentheses italic y minus sign 1 close parentheses end cell equals 0 row italic y equals cell negative sign 9 space atau space italic y equals 1 end cell end table end style

Untuk begin mathsize 14px style italic y equals minus sign 9 end style, kita dapatkan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row italic x equals cell 10 plus 2 italic y end cell row blank equals cell 10 plus 2 begin italic style left parenthesis straight minus sign straight 9 right parenthesis end style end cell row blank equals cell 10 minus sign 18 end cell row blank equals cell negative sign 8 end cell end table end style

Jadi, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell italic x minus sign italic y end cell equals cell negative sign 8 minus sign open parentheses negative sign 9 close parentheses end cell row blank equals cell negative sign 8 plus 9 end cell row blank equals 1 row blank blank blank end table end style

Kemudian, untuk begin mathsize 14px style italic y equals 1 end style, kita dapatkan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row italic x equals cell 10 plus 2 italic y end cell row blank equals cell 10 plus 2 begin italic style left parenthesis straight 1 right parenthesis end style end cell row blank equals cell 10 plus 2 end cell row blank equals 12 end table end style

Jadi, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell italic x minus sign italic y end cell equals cell 12 minus sign 1 end cell row blank equals 11 end table end style

Oleh karena itu, nilai yang mungkin dari begin mathsize 14px style italic x minus sign italic y end style adalah 1 atau 11.

Jadi, jawaban yang tepat adalah C.

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