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Dengan menggunakan vektor p​, vektor q​, dan vektor r pada soal Nomor 3, tentukanlah vektor x pada kesamaan-kesamaan vektor berikut. d. x+2q​+21​r=p​

Pertanyaan

Pada soal nomor 3, vektor p with rightwards arrow on top equals open parentheses table row 3 row 5 end table close parentheses, vektor q with rightwards arrow on top equals open parentheses table row 7 row cell negative 1 end cell end table close parentheses, dan vektor r with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 8 end table close parentheses.

Dengan menggunakan vektor p with rightwards arrow on top, vektor q with rightwards arrow on top, dan vektor r with rightwards arrow on top pada soal Nomor 3, tentukanlah vektor x with rightwards arrow on top pada kesamaan-kesamaan vektor berikut.

d. x with rightwards arrow on top plus 2 q with rightwards arrow on top plus 1 half r with rightwards arrow on top equals p with rightwards arrow on top

T. Prita

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jember

Jawaban terverifikasi

Jawaban

vektor x with rightwards arrow on top adalah open parentheses table row cell negative 9 end cell row 3 end table close parentheses.

Pembahasan

Jawaban yang benar dari pertanyaan tersebut adalah  vektor bold x with bold rightwards arrow on top adalah open parentheses table row cell negative 9 end cell row 3 end table close parentheses.

Hasil kali skalar dengan vektor di bidang. Misalkan m suatu skalar dan a with rightwards arrow on top equals open parentheses table row cell x subscript a end cell row cell y subscript a end cell end table close parentheses, hasil kali skalar m dengan vektor a with rightwards arrow on top ditulis sebagai c with rightwards arrow on top equals m a with rightwards arrow on top ditentukan oleh:

c with rightwards arrow on top equals m open parentheses table row cell x subscript a end cell row cell y subscript a end cell end table close parentheses equals open parentheses table row cell m x subscript a end cell row cell m y subscript a end cell end table close parentheses

Ingat kesamaan dua vektor di bidang, Misalkan diketahui vektor a with rightwards arrow on top equals open parentheses table row cell x subscript a end cell row cell y subscript a end cell end table close parentheses dan vektor b with rightwards arrow on top equals open parentheses table row cell x subscript b end cell row cell y subscript b end cell end table close parentheses. Vektor a with rightwards arrow on top equalsvektor b with rightwards arrow on top jika dan hanya jika x subscript a equals x subscript b dan y subscript a equals y subscript b.

Diketahui:
vektor p with rightwards arrow on top equals open parentheses table row 3 row 5 end table close parentheses
vektor q with rightwards arrow on top equals open parentheses table row 7 row cell negative 1 end cell end table close parentheses
vektor r with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 8 end table close parentheses

Misalkan:
vektor x with rightwards arrow on top equals open parentheses table row a row b end table close parentheses

Hasil perhitungan x with rightwards arrow on top plus 2 q with rightwards arrow on top plus 1 half r with rightwards arrow on top equals p with rightwards arrow on top:

table attributes columnalign right center left columnspacing 0px end attributes row cell x with rightwards arrow on top plus 2 q with rightwards arrow on top plus 1 half r with rightwards arrow on top end cell equals cell p with rightwards arrow on top end cell row cell open parentheses table row a row b end table close parentheses plus 2 open parentheses table row 7 row cell negative 1 end cell end table close parentheses plus 1 half open parentheses table row cell negative 4 end cell row 8 end table close parentheses end cell equals cell open parentheses table row 3 row 5 end table close parentheses end cell row cell open parentheses table row a row b end table close parentheses plus open parentheses table row cell open parentheses 2 close parentheses open parentheses 7 close parentheses end cell row cell open parentheses 2 close parentheses open parentheses negative 1 close parentheses end cell end table close parentheses plus open parentheses table row cell open parentheses 1 half close parentheses open parentheses negative 4 close parentheses end cell row cell open parentheses 1 half close parentheses open parentheses 8 close parentheses end cell end table close parentheses end cell equals cell open parentheses table row 3 row 5 end table close parentheses end cell row cell open parentheses table row a row b end table close parentheses plus open parentheses table row 14 row cell negative 2 end cell end table close parentheses plus open parentheses table row cell negative 2 end cell row 4 end table close parentheses end cell equals cell open parentheses table row 3 row 5 end table close parentheses end cell row cell open parentheses table row cell a plus 14 plus open parentheses negative 2 close parentheses end cell row cell b plus open parentheses negative 2 close parentheses plus 4 end cell end table close parentheses end cell equals cell open parentheses table row 3 row 5 end table close parentheses end cell row cell open parentheses table row cell a plus 12 end cell row cell b plus 2 end cell end table close parentheses end cell equals cell open parentheses table row 3 row 5 end table close parentheses end cell end table

Sehingga, untuk a:

table attributes columnalign right center left columnspacing 0px end attributes row cell a plus 12 end cell equals 3 row a equals cell 3 minus 12 end cell row a equals cell negative 9 end cell end table

Untuk b:

table attributes columnalign right center left columnspacing 0px end attributes row cell b plus 2 end cell equals 5 row b equals cell 5 minus 2 end cell row b equals 3 end table

Dengan demikian vektor x with rightwards arrow on top adalah open parentheses table row cell negative 9 end cell row 3 end table close parentheses.

30

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