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Diketahui , , dan . Jika , panjang vektor adalah ....

Diketahui begin mathsize 14px style u with rightwards arrow on top equals open parentheses table row 4 row cell negative 5 end cell row 3 end table close parentheses end stylebegin mathsize 14px style v with rightwards arrow on top equals open parentheses table row 2 row 2 row 1 end table close parentheses end style, dan begin mathsize 14px style w with rightwards arrow on top equals open parentheses table row 4 row 1 row cell negative 1 end cell end table close parentheses end style. Jika begin mathsize 14px style p with rightwards arrow on top equals u with rightwards arrow on top minus 2 v with rightwards arrow on top plus 3 w with rightwards arrow on top end style, panjang vektor size 14px p with size 14px rightwards arrow on top adalah ....

  1. begin mathsize 14px style 3 square root of 46 end style 

  2. begin mathsize 14px style square root of 46 end style 

  3. begin mathsize 14px style 2 square root of 23 end style 

  4. begin mathsize 14px style 2 square root of 46 end style 

  5. begin mathsize 14px style square root of 23 end style 

Jawaban:

Dengan menerapkan konsep penjumlahan vektor dan perkalian vektor dengan skalar, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p with rightwards arrow on top end cell equals cell u with rightwards arrow on top minus 2 v with rightwards arrow on top plus 3 w with rightwards arrow on top end cell row blank equals cell u with rightwards arrow on top plus open parentheses negative 2 v with rightwards arrow on top close parentheses plus 3 w with rightwards arrow on top end cell row blank equals cell open parentheses table row 4 row cell negative 5 end cell row 3 end table close parentheses plus open parentheses negative 2 close parentheses open parentheses table row 2 row 2 row 1 end table close parentheses plus 3 open parentheses table row 4 row 1 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 4 row cell negative 5 end cell row 3 end table close parentheses plus open parentheses table row cell negative 4 end cell row cell negative 4 end cell row cell negative 2 end cell end table close parentheses plus open parentheses table row 12 row 3 row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 12 row cell negative 6 end cell row cell negative 2 end cell end table close parentheses end cell end table end style 

Selanjutnya, dengan menerapkan rumus panjang vektor pada tiga dimensi, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell square root of 12 squared plus open parentheses negative 6 close parentheses squared plus open parentheses negative 2 close parentheses squared end root end cell row blank equals cell square root of 144 plus 36 plus 4 end root end cell row blank equals cell square root of 184 end cell row blank equals cell square root of 4 cross times 46 end root end cell row blank equals cell 2 square root of 46 end cell end table end style 

Dengan demikian, panjang vektor size 14px p with size 14px rightwards arrow on top adalah begin mathsize 14px style 2 square root of 46 end style.

Jadi, jawaban yang tepat adalah D.

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