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Diketahui vektor – vektor begin mathsize 14px style blank straight u with rightwards arrow on top equals 9 straight i with rightwards arrow on top plus straight a straight j with rightwards arrow on top plus straight b straight k with rightwards arrow on top end style dan begin mathsize 14px style straight v with rightwards arrow on top equals straight a straight i with rightwards arrow on top minus straight b straight j with rightwards arrow on top plus straight a straight k with rightwards arrow on top end style. Sudut antara vektor begin mathsize 14px style straight u end style dan vektor begin mathsize 14px style straight v end style adalah begin mathsize 14px style straight theta end style dengan begin mathsize 14px style cos invisible function application straight theta equals 6 over 11 end style. Proyeksi begin mathsize 14px style straight u end style pada begin mathsize 14px style straight v end style adalah begin mathsize 14px style straight p with rightwards arrow on top equals 4 straight i with rightwards arrow on top minus 2 straight j with rightwards arrow on top plus 4 straight k with rightwards arrow on top end style. Nilai b adalah ....

  1. undefined 

  2. undefined 

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

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

  5. begin mathsize 14px style 4 square root of 2 end style 

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.space space  

Pembahasan

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight u with rightwards arrow on top. straight v with rightwards arrow on top end cell equals cell open parentheses table row 9 row straight a row straight b end table close parentheses open parentheses table row straight a row cell negative straight b end cell row straight a end table close parentheses end cell row cell straight u with rightwards arrow on top. straight v with rightwards arrow on top end cell equals cell 9 straight a minus ab plus ab end cell row cell straight u with rightwards arrow on top. straight v with rightwards arrow on top end cell equals cell 9 straight a horizontal ellipsis horizontal ellipsis horizontal ellipsis open parentheses 1 close parentheses end cell end table end style  

Kemudian

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell blank straight u with rightwards arrow on top. straight v with rightwards arrow on top end cell equals cell open vertical bar straight u with rightwards arrow on top close vertical bar open vertical bar straight v with rightwards arrow on top close vertical bar cos invisible function application straight theta end cell row cell straight u with rightwards arrow on top. straight v with rightwards arrow on top end cell equals cell square root of 9 squared plus straight a squared plus straight b squared end root square root of straight a squared plus open parentheses negative straight b close parentheses squared plus straight a squared end root open parentheses 6 over 11 close parentheses end cell row cell straight u with rightwards arrow on top. straight v with rightwards arrow on top end cell equals cell square root of 9 squared plus straight a squared plus straight b squared end root square root of straight a squared plus straight b squared plus straight a squared end root open parentheses 6 over 11 close parentheses horizontal ellipsis horizontal ellipsis horizontal ellipsis open parentheses 2 close parentheses end cell end table end style 

Proyeksi begin mathsize 14px style straight u end style pada begin mathsize 14px style straight v end style adalah begin mathsize 14px style straight p with rightwards arrow on top equals 4 straight i with rightwards arrow on top minus 2 straight j with rightwards arrow on top plus 4 straight k with rightwards arrow on top end style, berarti

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight u with rightwards arrow on top. straight v with rightwards arrow on top over denominator open vertical bar straight v with rightwards arrow on top close vertical bar end fraction end cell equals cell square root of 4 squared plus open parentheses negative 2 close parentheses squared plus 4 squared end root end cell row cell fraction numerator straight u with rightwards arrow on top. straight v with rightwards arrow on top over denominator square root of straight a squared plus straight b squared plus straight a squared end root end fraction end cell equals 6 row cell straight u with rightwards arrow on top. straight v with rightwards arrow on top end cell equals cell 6 open parentheses square root of straight a squared plus straight b squared plus straight a squared end root close parentheses horizontal ellipsis horizontal ellipsis horizontal ellipsis open parentheses 3 close parentheses end cell end table end style 

Subtitusi persamaan (1) ke persamaan (3)

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 9 straight a end cell equals cell 6 open parentheses square root of straight a squared plus straight b squared plus straight a squared end root close parentheses end cell row cell 3 over 2 straight a end cell equals cell square root of straight a squared plus straight b squared plus straight a squared end root end cell row cell 9 over 4 straight a squared end cell equals cell straight a squared plus straight b squared plus straight a squared end cell row cell 1 fourth straight a squared end cell equals cell straight b squared end cell row cell straight a squared end cell equals cell 4 straight b squared end cell row straight a equals cell 2 straight b horizontal ellipsis horizontal ellipsis horizontal ellipsis open parentheses 4 close parentheses end cell end table end style 

Subitusi persamaan (4) dan (1) ke persamaan (2) :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 9 open parentheses 2 straight b close parentheses end cell equals cell square root of 9 squared plus 4 straight b squared plus straight b squared end root square root of 4 straight b squared plus straight b squared plus 4 straight b squared end root open parentheses 6 over 11 close parentheses end cell row cell 18 straight b end cell equals cell square root of 81 plus 5 straight b squared end root open parentheses 3 straight b close parentheses open parentheses 6 over 11 close parentheses end cell row cell fraction numerator 18 straight b over denominator 3 straight b end fraction open parentheses 11 over 6 close parentheses end cell equals cell square root of 81 plus 5 straight b squared end root end cell row 11 equals cell square root of 81 plus 5 straight b squared end root end cell row 121 equals cell 81 plus 5 straight b squared end cell row cell 5 straight b squared end cell equals 40 row cell straight b squared end cell equals 8 row straight b equals cell plus-or-minus 2 square root of 2 end cell end table end style 

Jadi, nilai b adalah begin mathsize 14px style plus-or-minus 2 square root of 2 end style

Jadi, jawaban yang tepat adalah D.space space  

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