Diketahui vektor , , dan . Vektor satuan yang searah dengan a−2b+c adalah ....

Pertanyaan

Diketahui vektor begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row 3 row 0 end table close parentheses end stylebegin mathsize 14px style b with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 5 end table close parentheses end style, dan begin mathsize 14px style c with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row 4 end table close parentheses end style. Vektor satuan yang searah dengan begin mathsize 14px style a with rightwards arrow on top minus 2 b with rightwards arrow on top plus c with rightwards arrow on top end style adalah ....

  1. begin mathsize 14px style open parentheses table row cell 1 half square root of 2 end cell row cell 1 half square root of 2 end cell end table close parentheses end style  

  2. begin mathsize 14px style open parentheses table row cell 1 half square root of 2 end cell row cell negative 1 half square root of 2 end cell end table close parentheses end style  

  3. begin mathsize 14px style open parentheses table row cell negative 1 half square root of 2 end cell row cell 1 half square root of 2 end cell end table close parentheses end style  

  4. begin mathsize 14px style open parentheses table row cell negative 1 half square root of 2 end cell row cell negative 1 half square root of 2 end cell end table close parentheses space space end style

  5. begin mathsize 14px style open parentheses table row 1 row 0 end table close parentheses end style  

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

Maka begin mathsize 14px style d with rightwards arrow on top equals a with rightwards arrow on top minus 2 b with rightwards arrow on top plus c with rightwards arrow on top end style. Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell d with rightwards arrow on top end cell equals cell a with rightwards arrow on top minus 2 b with rightwards arrow on top plus c with rightwards arrow on top end cell row blank equals cell open parentheses table row 3 row 0 end table close parentheses minus 2 open parentheses table row cell negative 2 end cell row 5 end table close parentheses plus open parentheses table row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row 3 row 0 end table close parentheses minus open parentheses table row cell negative 4 end cell row 10 end table close parentheses plus open parentheses table row cell negative 1 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 3 minus open parentheses negative 4 close parentheses plus open parentheses negative 1 close parentheses end cell row cell 0 minus 10 plus 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 6 row cell negative 6 end cell end table close parentheses end cell end table end style

Kemudian didapat bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar d with rightwards arrow on top close vertical bar end cell equals cell square root of 6 squared plus open parentheses negative 6 close parentheses squared end root end cell row blank equals cell square root of 36 plus 36 end root end cell row blank equals cell square root of 72 end cell row blank equals cell 6 square root of 2 end cell end table end style

Sehingga vektor satuan yang searah dengan begin mathsize 14px style d with rightwards arrow on top equals a with rightwards arrow on top minus 2 b with rightwards arrow on top plus c with rightwards arrow on top end style adalah

begin mathsize 14px style e subscript d with rightwards arrow on top end subscript equals fraction numerator d with rightwards arrow on top over denominator open vertical bar d with rightwards arrow on top close vertical bar end fraction equals fraction numerator 1 over denominator 6 square root of 2 end fraction open parentheses table row 6 row cell negative 6 end cell end table close parentheses equals open parentheses table row cell fraction numerator 6 over denominator 6 square root of 2 end fraction end cell row cell negative fraction numerator 6 over denominator 6 square root of 2 end fraction end cell end table close parentheses equals open parentheses table row cell fraction numerator 1 over denominator square root of 2 end fraction end cell row cell negative fraction numerator 1 over denominator square root of 2 end fraction end cell end table close parentheses equals open parentheses table row cell 1 half square root of 2 end cell row cell negative 1 half square root of 2 end cell end table close parentheses end style  

72

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