Pertanyaan

Diketahui vektor p = ⎝ ⎛ 2 4 6 ⎠ ⎞ dan q = ⎝ ⎛ 2 1 − 2 ⎠ ⎞ .Tentukan vektor satuan p dan q .

Diketahui vektor $\overline{p} = ⎝ ⎛ 246 ⎠ ⎞$ dan $\overline{q} = ⎝ ⎛ 21 - 2 ⎠ ⎞$ . Tentukan vektor satuan $\overline{p}$ dan $\overline{q}$ .

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Jawaban terverifikasi

Jawaban

dan .

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank Vektor end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank satuan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight p with bar on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell fraction numerator square root of 14 over denominator 14 end fraction comma end cell cell fraction numerator 2 square root of 14 over denominator 14 end fraction comma end cell cell fraction numerator 3 square root of 14 over denominator 14 end fraction end cell end table close parentheses end cell end table$ dan

Pembahasan

Misalkan adalah vektor, dan adalah panjang vektor, maka vektor satuan adalah Diketahui dan , maka vektor satuan adalah Vektor satuan yaitu Jadi, dan .

Misalkan top enclose straight a equals open parentheses table row cell straight a subscript 1 end cell cell straight a subscript 2 end cell end table close parentheses adalah vektor, dan open vertical bar top enclose a close vertical bar adalah panjang vektor, maka vektor satuan adalah

$Vektor space satuan space top enclose straight a equals fraction numerator top enclose straight a over denominator open vertical bar top enclose straight a close vertical bar end fraction equals fraction numerator open parentheses table row cell straight a subscript 1 end cell cell straight a subscript 2 end cell end table close parentheses over denominator open vertical bar top enclose straight a close vertical bar end fraction$

Diketahui straight p with bar on top equals open parentheses table row 2 row 4 row 6 end table close parentheses dan straight q with bar on top equals open parentheses table row 2 row 1 row cell negative 2 end cell end table close parentheses , maka vektor satuan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight p with bar on top end cell end table adalah

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight p with bar on top end cell equals cell fraction numerator straight p with bar on top over denominator open vertical bar straight p with bar on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses table row cell 2 comma end cell cell 4 comma end cell 6 end table close parentheses over denominator square root of 2 squared plus 4 squared plus 6 squared end root end fraction end cell row blank equals cell fraction numerator open parentheses table row cell 2 comma end cell cell 4 comma end cell 6 end table close parentheses over denominator square root of 4 plus 16 plus 36 end root end fraction end cell row blank equals cell fraction numerator open parentheses table row cell 2 comma end cell cell 4 comma end cell 6 end table close parentheses over denominator square root of 56 end fraction end cell row blank equals cell fraction numerator open parentheses table row cell 2 comma end cell cell 4 comma end cell 6 end table close parentheses over denominator square root of 4 cross times 14 end root end fraction end cell row blank equals cell fraction numerator open parentheses table row cell 2 comma end cell cell 4 comma end cell 6 end table close parentheses over denominator 2 square root of 14 end fraction end cell row blank equals cell open parentheses table row cell fraction numerator 2 over denominator 2 square root of 14 end fraction comma end cell cell fraction numerator 4 over denominator 2 square root of 14 end fraction comma end cell cell fraction numerator 6 over denominator 2 square root of 14 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator 1 over denominator square root of 14 end fraction comma end cell cell fraction numerator 2 over denominator square root of 14 end fraction comma end cell cell fraction numerator 3 over denominator square root of 14 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator square root of 14 over denominator 14 end fraction comma end cell cell fraction numerator 2 square root of 14 over denominator 14 end fraction comma end cell cell fraction numerator 3 square root of 14 over denominator 14 end fraction end cell end table close parentheses end cell end table$

Vektor satuan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight q with bar on top end cell end table yaitu

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight q with bar on top end cell equals cell fraction numerator straight q with bar on top over denominator open vertical bar straight q with bar on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses table row cell 2 comma end cell cell 1 comma end cell cell negative 2 end cell end table close parentheses over denominator square root of 2 squared plus 1 squared plus open parentheses negative 2 close parentheses squared end root end fraction end cell row blank equals cell fraction numerator open parentheses table row cell 2 comma end cell cell 1 comma end cell cell negative 2 end cell end table close parentheses over denominator square root of 4 plus 1 plus 4 end root end fraction end cell row blank equals cell fraction numerator open parentheses table row cell 2 comma end cell cell 1 comma end cell cell negative 2 end cell end table close parentheses over denominator square root of 9 end fraction end cell row blank equals cell fraction numerator open parentheses table row cell 2 comma end cell cell 1 comma end cell cell negative 2 end cell end table close parentheses over denominator 3 end fraction end cell row blank equals cell open parentheses table row cell 2 over 3 comma end cell cell 1 third comma end cell cell fraction numerator negative 2 over denominator 3 end fraction end cell end table close parentheses end cell end table$

Jadi, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank Vektor end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank satuan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight p with bar on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell fraction numerator square root of 14 over denominator 14 end fraction comma end cell cell fraction numerator 2 square root of 14 over denominator 14 end fraction comma end cell cell fraction numerator 3 square root of 14 over denominator 14 end fraction end cell end table close parentheses end cell end table$ dan .

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