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Titik-titik A(−1, 4, 8), B(1, 2, 3), dan C(5, y, z) segaris. Tentukan nilai-nilai y dan z.

Pertanyaan

Titik-titik straight A open parentheses negative 1 comma space 4 comma space 8 close parenthesesstraight B open parentheses 1 comma space 2 comma space 3 close parentheses, dan straight C open parentheses 5 comma space straight y comma space straight z close parentheses segaris. Tentukan nilai-nilai y dan z.space 

K. Prameswari

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

diperoleh nilai y dan z berturut-turut yaitu negative 2 dan negative 7 

Pembahasan

Diberikan tiga buah titik straight A open parentheses negative 1 comma space 4 comma space 8 close parenthesesstraight B open parentheses 1 comma space 2 comma space 3 close parentheses, dan straight C open parentheses 5 comma space straight y comma space straight z close parentheses. Dapat diperoleh vektor posisi stack O A with rightwards harpoon with barb upwards on topstack O B with rightwards harpoon with barb upwards on top, dan stack O C with rightwards harpoon with barb upwards on top berturut-turut yaitu

table attributes columnalign right center left columnspacing 0px end attributes row cell stack O A with rightwards harpoon with barb upwards on top end cell equals cell open parentheses negative 1 comma space 4 comma space 8 close parentheses end cell row cell stack O B with rightwards harpoon with barb upwards on top end cell equals cell open parentheses 1 comma space 2 comma space 3 close parentheses end cell row cell stack O C with rightwards harpoon with barb upwards on top end cell equals cell open parentheses 5 comma space y comma space z close parentheses end cell end table

Maka didapat

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards harpoon with barb upwards on top end cell equals cell stack O B with rightwards harpoon with barb upwards on top minus stack O A with rightwards harpoon with barb upwards on top end cell row blank equals cell open parentheses 1 comma space 2 comma space 3 close parentheses minus open parentheses negative 1 comma space 4 comma space 8 close parentheses end cell row blank equals cell open parentheses 1 minus open parentheses negative 1 close parentheses comma space 2 minus 4 comma space 3 minus 8 close parentheses end cell row blank equals cell open parentheses 2 comma space minus 2 comma space minus 5 close parentheses end cell row blank blank blank row cell stack B C with rightwards harpoon with barb upwards on top end cell equals cell stack O C with rightwards harpoon with barb upwards on top minus stack O B with rightwards harpoon with barb upwards on top end cell row blank equals cell open parentheses 5 comma space y comma space z close parentheses minus open parentheses 1 comma space 2 comma space 3 close parentheses end cell row blank equals cell open parentheses 5 minus 1 comma space y minus 2 comma space z minus 3 close parentheses end cell row blank equals cell open parentheses 4 comma space y minus 2 comma space z minus 3 close parentheses end cell end table

Ingat kembali bahwa apabila diberikan dua buah vektor bold italic a equals open parentheses a subscript 1 comma space a subscript 2 comma space a subscript 3 close parentheses dan bold italic b equals open parentheses b subscript 1 comma space b subscript 2 comma space b subscript 3 close parentheses dengan bold italic a equals bold italic b, maka berlaku

table attributes columnalign right center left columnspacing 0px end attributes row cell a subscript 1 end cell equals cell b subscript 1 end cell row cell a subscript 2 end cell equals cell b subscript 2 end cell row cell a subscript 3 end cell equals cell b subscript 3 end cell end table

Diketahui titik A, B, dan C segaris, artinya memenuhi stack A B with rightwards harpoon with barb upwards on top equals k stack B C with rightwards harpoon with barb upwards on top untuk suatu skalar k. Perhatikan bahwa

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards harpoon with barb upwards on top end cell equals cell k stack B C with rightwards harpoon with barb upwards on top end cell row cell open parentheses 2 comma space minus 2 comma space minus 5 close parentheses end cell equals cell k open parentheses 4 comma space y minus 2 comma space z minus 3 close parentheses end cell row cell open parentheses 2 comma space minus 2 comma space minus 5 close parentheses end cell equals cell open parentheses 4 k comma space k open parentheses y minus 2 close parentheses comma space k open parentheses z minus 3 close parentheses close parentheses end cell end table

Berarti

table attributes columnalign right center left columnspacing 0px end attributes row 2 equals cell 4 k end cell row cell 2 over 4 end cell equals k row cell 1 half end cell equals k end table

Akibatnya didapat

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 2 end cell equals cell k open parentheses y minus 2 close parentheses end cell row cell negative 2 end cell equals cell 1 half open parentheses y minus 2 close parentheses end cell row cell negative 2 cross times 2 end cell equals cell y minus 2 end cell row cell negative 4 end cell equals cell y minus 2 end cell row cell negative 4 plus 2 end cell equals y row cell negative 2 end cell equals y row blank blank blank row cell negative 5 end cell equals cell k open parentheses z minus 3 close parentheses end cell row cell negative 5 end cell equals cell 1 half open parentheses z minus 3 close parentheses end cell row cell negative 5 cross times 2 end cell equals cell z minus 3 end cell row cell negative 10 end cell equals cell z minus 3 end cell row cell negative 10 plus 3 end cell equals z row cell negative 7 end cell equals z end table

Dengan demikian, diperoleh nilai y dan z berturut-turut yaitu negative 2 dan negative 7 

220

4.6 (5 rating)

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