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Pertanyaan

Diketahui . Jika u = 2 a + 2 b − 2 c , maka vektor satuan dari u adalah ….

Diketahui begin mathsize 14px style straight a with rightwards arrow on top equals open parentheses table row 1 row cell negative 1 end cell row 2 end table close parentheses comma blank straight b with rightwards arrow on top equals open parentheses table row 1 row 4 row cell negative 3 end cell end table close parentheses comma blank dan blank straight c with rightwards arrow on top equals open parentheses table row 4 row 1 row cell negative 2 end cell end table close parentheses end style. Jika , maka vektor satuan dari  adalah ….

  1. begin mathsize 14px style 1 third open parentheses table row cell negative 4 end cell row 4 row 2 end table close parentheses end style 

  2. begin mathsize 14px style 1 third open parentheses table row cell negative 2 end cell row 2 row 1 end table close parentheses end style 

  3. begin mathsize 14px style 1 over 6 open parentheses table row 2 row cell negative 2 end cell row 1 end table close parentheses end style 

  4. begin mathsize 14px style 1 over 6 open parentheses table row cell negative 2 end cell row 2 row 1 end table close parentheses end style 

  5. begin mathsize 14px style 1 half open parentheses table row cell negative 4 end cell row 4 row 2 end table close parentheses end style 

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

jawaban yang tepat adalah B.space space  

Pembahasan

Perhatikan bahwa, Sehingga, Diperoleh vektor satuan adalah Jadi, jawaban yang tepat adalah B.

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 end cell equals cell 2 straight a with rightwards arrow on top plus 2 straight b with rightwards arrow on top minus 2 straight c with rightwards arrow on top end cell row blank equals cell 2 open parentheses table row 1 row cell negative 1 end cell row 2 end table close parentheses plus 2 open parentheses table row 1 row 4 row cell negative 3 end cell end table close parentheses minus 2 open parentheses table row 4 row 1 row cell negative 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell negative 2 end cell row 4 end table close parentheses plus open parentheses table row 2 row 8 row cell negative 6 end cell end table close parentheses minus open parentheses table row 8 row 2 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 2 plus 2 minus 8 end cell row cell negative 2 plus 8 minus 2 end cell row cell 4 plus open parentheses negative 6 close parentheses minus open parentheses negative 4 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell row 4 row 2 end table close parentheses end cell end table end style 

Sehingga,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight u with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 4 close parentheses squared plus open parentheses 4 close parentheses squared plus open parentheses 2 close parentheses squared end root end cell row blank equals cell square root of 16 plus 16 plus 4 end root end cell row blank equals cell square root of 36 end cell row blank equals 6 end table end style 

Diperoleh vektor satuan undefined adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight e subscript straight u with rightwards arrow on top end subscript end cell equals cell fraction numerator straight u with rightwards arrow on top over denominator open vertical bar straight u with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses table row cell negative 4 end cell row 4 row 2 end table close parentheses over denominator 6 end fraction end cell row blank equals cell 1 over 6 open parentheses table row cell negative 4 end cell row 4 row 2 end table close parentheses end cell row blank equals cell 1 over 6 times 2 open parentheses table row cell negative 2 end cell row 2 row 1 end table close parentheses end cell row blank equals cell 1 third open parentheses table row cell negative 2 end cell row 2 row 1 end table close parentheses end cell end table end style 

Jadi, jawaban yang tepat adalah B.space space  

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