Pertanyaan

Misalkan vektor a ⇀ = ( − 3 x ) . Tentukan nilai x yang mungkin jika vektor satuan dari vektor a ⇀ adalah ( 5 − 3 5 x ) .

Misalkan vektor $a ⇀ = (- 3 x)$ . Tentukan nilai $x$ yang mungkin jika vektor satuan dari vektor $a ⇀$ adalah $(\frac{- 3}{5} \frac{x}{5})$ .

R. RGFLLIMA

Master Teacher

Jawaban terverifikasi

Jawaban

Jika vektor makanilai yang mungkin jika vektor satuan dari vektor adalah

Jika vektor begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals open parentheses table row cell negative 3 end cell row straight x end table close parentheses end style

begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals open parentheses table row cell negative 3 end cell row straight x end table close parentheses end style

maka nilai begin mathsize 14px style x end style

yang mungkin jika vektor satuan dari vektor begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals end style

begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals end style

$begin mathsize 14px style open parentheses table row cell fraction numerator negative 3 over denominator 5 end fraction end cell row cell straight x over 5 end cell end table close parentheses end style$ adalah begin mathsize 14px style straight x equals plus-or-minus 4. end style

begin mathsize 14px style straight x equals plus-or-minus 4. end style

Pembahasan

Vektor satuan. Diketahui: vektor maka vektor satuan maka: Dari kesamaan 2 vektor sehingga diperoleh: Jadi, Jika vektor makanilai yang mungkin jika vektor satuan dari vektor adalah

Vektor satuan.

Diketahui:

vektor begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals open parentheses table row cell negative 3 end cell row straight x end table close parentheses end style

maka

vektor satuan $begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals fraction numerator straight a with rightwards harpoon with barb upwards on top over denominator open vertical bar straight a with rightwards harpoon with barb upwards on top close vertical bar end fraction end style$ maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell fraction numerator negative 3 over denominator 5 end fraction end cell row cell straight x over 5 end cell end table close parentheses end cell equals cell fraction numerator open parentheses table row cell negative 3 end cell row straight x end table close parentheses over denominator square root of left parenthesis negative 3 right parenthesis squared plus straight x to the power of 2 end exponent end root end fraction end cell row cell open parentheses table row cell fraction numerator negative 3 over denominator 5 end fraction end cell row cell straight x over 5 end cell end table close parentheses end cell equals cell fraction numerator open parentheses table row cell negative 3 end cell row straight x end table close parentheses over denominator square root of 9 plus straight x squared end root end fraction end cell row cell open parentheses table row cell fraction numerator negative 3 over denominator 5 end fraction end cell row cell straight x over 5 end cell end table close parentheses end cell equals cell open parentheses table row cell fraction numerator negative 3 over denominator square root of 9 plus straight x squared end root end fraction end cell row cell fraction numerator straight x over denominator square root of 9 plus straight x squared end root end fraction end cell end table close parentheses end cell row blank blank blank end table end style$

Dari kesamaan 2 vektor sehingga diperoleh:

Jadi, Jika vektor begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals open parentheses table row cell negative 3 end cell row straight x end table close parentheses end style maka nilai begin mathsize 14px style x end style yang mungkin jika vektor satuan dari vektor $begin mathsize 14px style open parentheses table row cell fraction numerator negative 3 over denominator 5 end fraction end cell row cell straight x over 5 end cell end table close parentheses end style$ adalah begin mathsize 14px style straight x equals plus-or-minus 4. end style