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Pertanyaan

Diketahui sudut antara vektor a dan b adalah 45° . Jika a . a = 5 dan a . b = 20 maka b . ( a − b ) = ....

Diketahui sudut antara vektor  dan  adalah 45°. Jika  dan  maka

  1. -180

  2. -140

  3. 80

  4. 140

  5. 180

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Master Teacher

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Pembahasan

Karena maka Karena panjang vektor tidak mungkin negatif, maka Kemudian sudut antara vektor dan adalah 45° . Sehingga Sehingga

Karena begin mathsize 14px style straight a with rightwards arrow on top space. space straight a with rightwards arrow on top equals 5 end style maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top space. space straight a with rightwards arrow on top end cell equals 5 row cell open vertical bar straight a with rightwards arrow on top close vertical bar squared end cell equals 5 row cell open vertical bar straight a with rightwards arrow on top close vertical bar end cell equals cell plus-or-minus square root of 5 end cell end table end style 

Karena panjang vektor tidak mungkin negatif, maka begin mathsize 14px style open vertical bar straight a with rightwards arrow on top close vertical bar equals square root of 5 end style

Kemudian sudut antara vektor undefined dan undefined adalah 45° . Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top space. space straight b with rightwards arrow on top end cell equals cell stack open vertical bar straight a close vertical bar with rightwards arrow on top space open vertical bar straight b with rightwards arrow on top close vertical bar space cos space 45 degree end cell row 20 equals cell square root of 5 space. space open vertical bar straight b with rightwards arrow on top close vertical bar space. space 1 half square root of 2 end cell row 20 equals cell 1 half square root of 10 space. space open vertical bar straight b with rightwards arrow on top close vertical bar end cell row cell open vertical bar straight b with rightwards arrow on top close vertical bar end cell equals cell fraction numerator 40 over denominator square root of 10 end fraction end cell row cell open vertical bar straight b with rightwards arrow on top close vertical bar end cell equals cell 40 over 10 square root of 10 end cell row cell open vertical bar straight b with rightwards arrow on top close vertical bar end cell equals cell 4 square root of 10 end cell end table end style 

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight b with rightwards arrow on top space. space open parentheses straight a with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses end cell equals cell straight b with rightwards arrow on top space. space straight a with rightwards arrow on top minus straight b with rightwards arrow on top space. space straight b with rightwards arrow on top end cell row blank equals cell straight b with rightwards arrow on top space. space straight a with rightwards arrow on top minus open vertical bar straight b with rightwards arrow on top close vertical bar squared end cell row blank equals cell 20 minus open parentheses 4 square root of 10 close parentheses squared end cell row blank equals cell 20 minus 160 end cell row blank equals cell negative 140 end cell end table end style 

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