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Pertanyaan

Diketahui vektor p ​ = ⎝ ⎛ ​ 2 − 4 − 1 ​ ⎠ ⎞ ​ dan q ​ = ⎝ ⎛ ​ − 3 1 − 2 ​ ⎠ ⎞ ​ . Jika koordinat titik B ( 4 , − 2 , 3 ) dan AB = 2 p ​ − 3 q ​ , tentukan koordinat titik A .

Diketahui vektor  dan . Jika koordinat titik  dan , tentukan koordinat titik .

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M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

koordinat titik adalah .

 koordinat titik begin mathsize 14px style straight A end style adalah begin mathsize 14px style open parentheses negative 9 comma space 9 comma space minus 1 close parentheses end style.

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Pembahasan

Diketahui: , , dan Maka: Jadi,koordinat titik adalah .

Diketahui:

begin mathsize 14px style straight p with rightwards arrow on top equals open parentheses table row 2 row cell negative 4 end cell row cell negative 1 end cell end table close parentheses end stylebegin mathsize 14px style straight q with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row 1 row cell negative 2 end cell end table close parentheses end stylebegin mathsize 14px style straight B open parentheses 4 comma space minus 2 comma space 3 close parentheses end style dan begin mathsize 14px style AB with rightwards arrow on top equals 2 straight p with rightwards arrow on top minus 3 straight q with rightwards arrow on top end style

Maka:

begin mathsize 14px style space space space space space space space space space space AB with rightwards arrow on top equals 2 straight p with rightwards arrow on top minus 3 straight q with rightwards arrow on top space space space space space space straight b with rightwards arrow on top minus straight a with rightwards arrow on top equals 2 straight p with rightwards arrow on top minus 3 straight q with rightwards arrow on top open parentheses table row 4 row cell negative 2 end cell row 3 end table close parentheses minus straight a with rightwards arrow on top equals 2 open parentheses table row 2 row cell negative 4 end cell row cell negative 1 end cell end table close parentheses minus 3 open parentheses table row cell negative 3 end cell row 1 row cell negative 2 end cell end table close parentheses open parentheses table row 4 row cell negative 2 end cell row 3 end table close parentheses minus straight a with rightwards arrow on top equals open parentheses table row 4 row cell negative 8 end cell row cell negative 2 end cell end table close parentheses minus open parentheses table row cell negative 9 end cell row 3 row cell negative 6 end cell end table close parentheses open parentheses table row 4 row cell negative 2 end cell row 3 end table close parentheses minus straight a with rightwards arrow on top equals open parentheses table row 13 row cell negative 11 end cell row 4 end table close parentheses space space space space space space space space space space space space space straight a with rightwards arrow on top equals open parentheses table row 4 row cell negative 2 end cell row 3 end table close parentheses minus open parentheses table row 13 row cell negative 11 end cell row 4 end table close parentheses space space space space space space space space space space space space space straight a with rightwards arrow on top equals open parentheses table row cell negative 9 end cell row 9 row cell negative 1 end cell end table close parentheses end style  

Jadi, koordinat titik begin mathsize 14px style straight A end style adalah begin mathsize 14px style open parentheses negative 9 comma space 9 comma space minus 1 close parentheses end style.

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