Diketahui vektor dan titik . Jika panjang sama dengan panjang dan berlawanan arah dengan , maka tentukan koordinat Q.

Diketahui vektor $begin mathsize 14px style a with rightwards harpoon with barb upwards on top equals 4 i with rightwards harpoon with barb upwards on top minus 5 j with rightwards harpoon with barb upwards on top plus 3 k with rightwards harpoon with barb upwards on top end style$ dan titik $begin mathsize 14px style P open parentheses 2 comma negative 1 comma 3 close parentheses end style$ . Jika panjang $begin mathsize 14px style stack P Q with rightwards harpoon with barb upwards on top end style$ sama dengan panjang $begin mathsize 14px style a with rightwards harpoon with barb upwards on top end style$ dan $begin mathsize 14px style stack P Q with rightwards harpoon with barb upwards on top end style$ berlawanan arah dengan $begin mathsize 14px style a with rightwards harpoon with barb upwards on top end style$ , maka tentukan koordinat Q.

Jawaban:

Ingat vektor yang menghubungkan dua titik diperoleh dari koordinat titik akhir dikurangi titik awal.

panjang $begin mathsize 14px style stack P Q with rightwards harpoon with barb upwards on top end style$ sama dengan panjang $begin mathsize 14px style a with rightwards harpoon with barb upwards on top end style$ dan $begin mathsize 14px style stack P Q with rightwards harpoon with barb upwards on top end style$ berlawanan arah dengan $begin mathsize 14px style a with rightwards harpoon with barb upwards on top end style$ , artinya

$begin mathsize 14px style stack P Q with rightwards harpoon with barb upwards on top equals negative a with bar on top end style$

$begin mathsize 14px style q with bar on top minus p with bar on top equals negative a with bar on top end style$

$begin mathsize 14px style q with bar on top equals p with bar on top minus a with bar on top end style$

$begin mathsize 14px style q with bar on top equals open parentheses table row 2 row cell negative 1 end cell row 3 end table close parentheses minus open parentheses table row 4 row cell negative 5 end cell row 3 end table close parentheses equals open parentheses table row cell negative 2 end cell row 4 row 0 end table close parentheses end style$

Jadi koordinat titik Q adalah $begin mathsize 14px style open parentheses negative 2 comma 4 comma 0 close parentheses end style$ .

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