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Diketahui vektor u = ⎝ ⎛ ​ 2 1 ​ 4 3 ​ x ​ ⎠ ⎞ ​ dan v = ⎝ ⎛ ​ 4 1 ​ x y ​ ⎠ ⎞ ​ adalah vektor satuan. Panjang dari vektor p ​ = ⎝ ⎛ ​ x 2 3 ​ y ​ ⎠ ⎞ ​ adalah ....

Diketahui vektor  dan  adalah vektor satuan. Panjang dari vektor
 adalah ....

  1. begin mathsize 14px style fraction numerator square root of 51 over denominator 2 end fraction end style 

  2. begin mathsize 14px style fraction numerator square root of 51 over denominator 4 end fraction end style 

  3. begin mathsize 14px style fraction numerator square root of 51 over denominator 8 end fraction end style 

  4. begin mathsize 14px style fraction numerator square root of 17 over denominator 4 end fraction end style 

  5. begin mathsize 14px style fraction numerator square root of 17 over denominator 8 end fraction end style 

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Pembahasan

Vektor merupakan vektor satuan. Sehingga Kemudian juga merupakan vektor satuan. Sehingga Sehingga panjang dari vektor adalah

Vektor begin mathsize 14px style straight u with rightwards arrow on top end style merupakan vektor satuan. 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 1 row cell square root of open parentheses 1 half close parentheses squared plus open parentheses 3 over 4 close parentheses squared plus straight x squared end root end cell equals 1 row cell square root of 1 fourth plus 9 over 16 plus straight x squared end root end cell equals 1 row cell square root of 14 over 16 plus 9 over 16 plus straight x squared end root end cell equals 1 row cell square root of 13 over 16 plus straight x squared end root end cell equals 1 row cell 13 over 16 plus straight x squared end cell equals 1 row cell straight x squared end cell equals cell 1 minus 13 over 16 end cell row cell straight x squared end cell equals cell 3 over 16 end cell end table end style 

Kemudian begin mathsize 14px style straight v with rightwards arrow on top end style juga merupakan vektor satuan. Sehingga

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 1 row cell square root of open parentheses 1 fourth close parentheses squared plus straight x squared plus straight y squared end root end cell equals 1 row cell square root of 1 over 16 plus 3 over 16 plus straight y squared end root end cell equals 1 row cell square root of 14 over 16 plus straight y squared end root end cell equals 1 row cell straight y squared end cell equals cell 1 minus 14 over 16 end cell row cell straight y squared end cell equals cell 12 over 16 end cell end table end style 

Sehingga panjang dari vektor begin mathsize 14px style straight p with rightwards arrow on top equals open parentheses table row straight x row cell 3 over 2 end cell row straight y end table close parentheses end style adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight p close vertical bar end cell equals cell square root of straight x squared plus open parentheses 3 over 2 close parentheses squared plus straight y squared end root end cell row blank equals cell square root of 3 over 16 plus 9 over 4 plus 12 over 16 end root end cell row blank equals cell square root of 3 over 16 plus 36 over 16 plus 12 over 16 end root end cell row blank equals cell square root of 51 over 16 end root end cell row blank equals cell fraction numerator square root of 51 over denominator 4 end fraction end cell end table end style 

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