Diketahui , , dan . Jika maka tentukan panjang !

Diketahui $begin mathsize 14px style straight d with rightwards arrow on top equals open parentheses table row cell negative 7 end cell row 3 row 5 end table close parentheses end style$ , $begin mathsize 14px style straight e with rightwards arrow on top equals open parentheses table row 3 row cell negative 5 end cell row 4 end table close parentheses end style$ , dan $begin mathsize 14px style straight f with rightwards arrow on top equals open parentheses table row 1 row cell negative 7 end cell row 4 end table close parentheses end style$ . Jika $begin mathsize 14px style straight v with rightwards arrow on top equals straight d with rightwards arrow on top minus 2 straight e with rightwards arrow on top plus 3 straight f with rightwards arrow on top end style$ maka tentukan panjang $begin mathsize 14px style straight v with rightwards arrow on top end style$ !

Jawaban:

Berdasarkan konsep penjumlahan vektor tiga dimensi maka diperoleh vektor $begin mathsize 14px style straight v with rightwards arrow on top end style$ :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight v with rightwards arrow on top end cell equals cell straight d with rightwards arrow on top minus 2 straight e with rightwards arrow on top plus 3 straight f with rightwards arrow on top end cell row blank equals cell open parentheses table row cell negative 7 end cell row 3 row 5 end table close parentheses minus 2 open parentheses table row 3 row cell negative 5 end cell row 4 end table close parentheses plus 3 open parentheses table row 1 row cell negative 7 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 7 end cell row 3 row 5 end table close parentheses minus open parentheses table row 6 row cell negative 10 end cell row 8 end table close parentheses plus open parentheses table row 3 row cell negative 21 end cell row 12 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 7 minus 6 plus 3 end cell row cell 3 minus open parentheses negative 10 close parentheses plus open parentheses negative 21 close parentheses end cell row cell 5 minus 8 plus 12 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 10 end cell row cell negative 8 end cell row 9 end table close parentheses end cell end table end style$

Sehingga panjang vektor $begin mathsize 14px style straight v with rightwards arrow on top end style$ adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight v with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 10 close parentheses squared plus open parentheses negative 8 close parentheses squared plus 9 squared end root end cell row blank equals cell square root of 100 plus 64 plus 81 end root end cell row blank equals cell square root of 245 end cell row blank equals cell square root of 49 cross times 5 end root end cell row blank equals cell 7 square root of 5 end cell end table end style$

Dengan demikian, panjang vektor $begin mathsize 14px style straight v with rightwards arrow on top end style$ adalah $begin mathsize 14px style 7 square root of 5 end style$ .

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