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Diketahui segitiga  dengan koordinat , dan . Tentukan: b. Panjang Vektor , dan

Pertanyaan

Diketahui segitiga ABC dengan koordinat straight A open parentheses 2 comma space minus 3 close parentheses comma space straight B open parentheses 5 comma space 0 close parentheses, dan straight C open parentheses 4 comma space 2 close parentheses. Tentukan:

b. Panjang Vektor AB comma space BC, dan CA 

Pembahasan Soal:

Diketahui segitiga ABC dengan koordinat straight A open parentheses 2 comma space minus 3 close parentheses comma space straight B open parentheses 5 comma space 0 close parentheses, dan straight C open parentheses 4 comma space 2 close parentheses. Maka:

straight a with rightwards arrow on top equals open parentheses table row 2 row cell negative 3 end cell end table close parentheses comma space straight b with rightwards arrow on top equals open parentheses table row 5 row 0 end table close parentheses comma space straight c with rightwards arrow on top equals open parentheses table row 4 row 2 end table close parentheses 

Sehingga:

AB with rightwards arrow on top equals straight b with rightwards arrow on top minus straight a with rightwards arrow on top equals open parentheses table row 5 row 0 end table close parentheses minus open parentheses table row 2 row cell negative 3 end cell end table close parentheses equals open parentheses table row 3 row 3 end table close parentheses BC with rightwards arrow on top equals straight c with rightwards arrow on top minus straight b with rightwards arrow on top equals open parentheses table row 4 row 2 end table close parentheses minus open parentheses table row 5 row 0 end table close parentheses equals open parentheses table row cell negative 1 end cell row 2 end table close parentheses CA with rightwards arrow on top equals straight a with rightwards arrow on top minus straight c with rightwards arrow on top equals open parentheses table row 2 row cell negative 3 end cell end table close parentheses minus open parentheses table row 4 row 2 end table close parentheses equals open parentheses table row cell negative 2 end cell row cell negative 5 end cell end table close parentheses 

Kemudian:

open vertical bar AB with rightwards arrow on top close vertical bar equals square root of 3 squared plus 3 squared end root equals square root of 9 plus 9 end root equals square root of 18 equals square root of 9 cross times 2 end root equals 3 square root of 2 open vertical bar BC with rightwards arrow on top close vertical bar equals square root of open parentheses negative 1 close parentheses squared plus 2 squared end root equals square root of 1 plus 4 end root equals square root of 5 open vertical bar CA with rightwards arrow on top close vertical bar equals square root of open parentheses negative 2 close parentheses squared plus open parentheses negative 5 close parentheses squared end root equals square root of 4 plus 25 end root equals square root of 29 

Jadi, panjang vektor AB comma space BC, dan CA adalah 3 square root of 2 comma space square root of 5, dan square root of 29.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Juni 2021

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