Diketahui A(6,0), B(−3,−4), C(5,2). Tentukan panjang vector AB, BC dan AC serta vector satuan yang searah dengan vector

Pertanyaan

Diketahui $\style{font-size:14px}{\mathrm A(6,\;0)}$ , $\style{font-size:14px}{\mathrm B(-3,\;-\;4)}$ , $\style{font-size:14px}{\mathrm C(5,\;2)}$ . Tentukan panjang vector $\style{font-size:14px}{\mathrm{AB}}$ , $\style{font-size:14px}{\mathrm{BC}}$ dan $\style{font-size:14px}{\mathrm{AC}}$ serta vector satuan yang searah dengan vector $undefined$

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... $undefined$

Pembahasan:

Vektor $undefined$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell straight B minus straight A end cell row blank equals cell open parentheses table row cell negative 3 end cell row cell negative 4 end cell end table close parentheses minus open parentheses table row 6 row 0 end table close parentheses end cell row cell stack A B with rightwards arrow on top end cell equals cell open parentheses table row cell negative 9 end cell row cell negative 4 end cell end table close parentheses end cell end table end style$

Panjang vektor $begin mathsize 14px style stack A B with rightwards arrow on top end style$ adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack A B with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 9 close parentheses squared plus open parentheses negative 4 close parentheses squared end root end cell row blank equals cell square root of 81 plus 16 end root end cell row cell open vertical bar stack A B with rightwards arrow on top close vertical bar end cell equals cell square root of 97 end cell end table end style$

Vektor $begin mathsize 14px style stack B C with rightwards arrow on top end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack B C with rightwards arrow on top end cell equals cell straight C minus straight B end cell row blank equals cell open parentheses table row 5 row 2 end table close parentheses minus open parentheses table row cell negative 3 end cell row cell negative 4 end cell end table close parentheses end cell row cell stack B C with rightwards arrow on top end cell equals cell open parentheses table row 8 row 6 end table close parentheses end cell end table end style$

Panjang vektor $undefined$ adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack B C with rightwards arrow on top close vertical bar end cell equals cell square root of 8 squared plus 6 squared end root end cell row blank equals cell square root of 64 plus 36 end root end cell row blank equals cell square root of 100 end cell row cell open vertical bar stack B C with rightwards arrow on top close vertical bar end cell equals 10 end table end style$

Vektor $begin mathsize 14px style stack A C with rightwards arrow on top end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack A C with rightwards arrow on top end cell equals cell straight C minus straight A end cell row blank equals cell open parentheses table row 5 row 2 end table close parentheses minus open parentheses table row 6 row 0 end table close parentheses end cell row cell stack A C with rightwards arrow on top end cell equals cell open parentheses table row cell negative 1 end cell row 2 end table close parentheses end cell end table end style$

Panjang vektor $undefined$ adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack A C with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 1 close parentheses squared plus 2 squared end root end cell row blank equals cell square root of 1 plus 4 end root end cell row cell open vertical bar stack A C with rightwards arrow on top close vertical bar end cell equals cell square root of 5 end cell end table end style$

Vektor satuan yang searah dengan $undefined$ adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack B C with rightwards arrow on top end cell equals cell fraction numerator stack B C with rightwards arrow on top over denominator open vertical bar stack B C with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell 1 over 10 open parentheses negative 3 comma space minus 4 close parentheses end cell row cell stack B C with rightwards arrow on top end cell equals cell open parentheses fraction numerator negative 3 over denominator 10 end fraction comma space fraction numerator negative 4 over denominator 10 end fraction close parentheses end cell end table end style$

Dengan demikian panjang vektor $begin mathsize 14px style stack A B with rightwards arrow on top comma space stack B C with rightwards arrow on top end style$ dan $undefined$ serta vektor satuan yang searah dengan vektor $undefined$ adalah $begin mathsize 14px style square root of 97 comma space 10 end style$ dan $begin mathsize 14px style square root of 5 end style$ serta $begin mathsize 14px style open parentheses fraction numerator negative 3 over denominator 10 end fraction comma space fraction numerator negative 4 over denominator 10 end fraction close parentheses end style$ .

Jawaban terverifikasi

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Terakhir diupdate 05 Oktober 2021