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Pertanyaan

Diketahui vektor a with rightwards arrow on top equals open parentheses table row 3 row cell negative 2 end cell end table close parentheses, vektor b with rightwards arrow on top equals open parentheses table row 4 row 1 end table close parentheses, dan vektor c with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row cell negative 1 end cell end table close parentheses berlaku hubungan 2 a with rightwards arrow on top minus 3 b with rightwards arrow on top plus x c with rightwards arrow on top equals open parentheses table row 0 row cell negative 4 end cell end table close parentheses, dengan x element of text bilangan real end text. Tentukanlah nilai x.

T. Prita

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jember

Jawaban terverifikasi

Jawaban

nilai x adalah negative 3.

Pembahasan

Jawaban yang benar dari pertanyaan tersebut adalah bold minus bold 3.

Penulisan vektor dalam bentuk r with rightwards arrow on top equals x i with hat on top plus y j with hat on top dapat dinyatakan dalam bentuk vektor baris sebagai r with rightwards arrow on top equals open parentheses table row x y end table close parentheses atau vektor kolom sebagai r with rightwards arrow on top equals open parentheses table row x row y end table close parentheses.

Ingat teori mengenai penjumlahan vektor. Penjumlahan vektor secara aljabar dapat dilakukan dengan cara menjumlahkan komponen yang seletak. 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 . Jika c with rightwards arrow on top equals a with rightwards arrow on top plus b with rightwards arrow on top, maka vektor c with rightwards arrow on top ditentukan oleh:

c 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 plus open parentheses table row cell x subscript b end cell row cell y subscript b end cell end table close parentheses equals open parentheses table row cell x subscript a plus x subscript b end cell row cell y subscript a plus y subscript b end cell end table close parentheses

Begitupun dengan pengurangan vektor, jika c with rightwards arrow on top equals a with rightwards arrow on top minus b with rightwards arrow on top maka vektor c with rightwards arrow on top ditentukan oleh:

c 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 minus open parentheses table row cell x subscript b end cell row cell y subscript b end cell end table close parentheses equals open parentheses table row cell x subscript a minus x subscript b end cell row cell y subscript a minus y subscript b end cell end table close parentheses

Selanjutnya hasil skalar dengan vektor. Misalkan m adalah suatu skalar dan a with rightwards arrow on top adalah vektor dengan 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

Diketahui:
vektor a with rightwards arrow on top equals open parentheses table row 3 row cell negative 2 end cell end table close parentheses
vektor b with rightwards arrow on top equals open parentheses table row 4 row 1 end table close parentheses
vektor c with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row cell negative 1 end cell end table close parentheses
2 a with rightwards arrow on top minus 3 b with rightwards arrow on top plus x c with rightwards arrow on top equals open parentheses table row 0 row cell negative 4 end cell end table close parentheses, dengan x element of text bilangan real end text

Nilai x dapat ditentukan dengan:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a with rightwards arrow on top minus 3 b with rightwards arrow on top plus x c with rightwards arrow on top end cell equals cell open parentheses table row 0 row cell negative 4 end cell end table close parentheses end cell row cell 2 open parentheses table row 3 row cell negative 2 end cell end table close parentheses minus 3 open parentheses table row 4 row 1 end table close parentheses plus x open parentheses table row cell negative 2 end cell row cell negative 1 end cell end table close parentheses end cell equals cell open parentheses table row 0 row cell negative 4 end cell end table close parentheses end cell row cell open parentheses table row cell open parentheses 2 close parentheses open parentheses 3 close parentheses end cell row cell open parentheses 2 close parentheses open parentheses negative 2 close parentheses end cell end table close parentheses minus open parentheses table row cell open parentheses 3 close parentheses open parentheses 4 close parentheses end cell row cell open parentheses 3 close parentheses open parentheses 1 close parentheses end cell end table close parentheses plus open parentheses table row cell open parentheses x close parentheses open parentheses negative 2 close parentheses end cell row cell open parentheses x close parentheses open parentheses negative 1 close parentheses end cell end table close parentheses end cell equals cell open parentheses table row 0 row cell negative 4 end cell end table close parentheses end cell row cell open parentheses table row 6 row cell negative 4 end cell end table close parentheses minus open parentheses table row 12 row 3 end table close parentheses plus open parentheses table row cell negative 2 x end cell row cell negative x end cell end table close parentheses end cell equals cell open parentheses table row 0 row cell negative 4 end cell end table close parentheses end cell row cell open parentheses table row cell 6 minus 12 plus open parentheses negative 2 x close parentheses end cell row cell negative 4 minus 3 plus open parentheses negative x close parentheses end cell end table close parentheses end cell equals cell open parentheses table row 0 row cell negative 4 end cell end table close parentheses end cell row cell open parentheses table row cell negative 6 plus open parentheses negative 2 x close parentheses end cell row cell negative 7 plus open parentheses negative x close parentheses end cell end table close parentheses end cell equals cell open parentheses table row 0 row cell negative 4 end cell end table close parentheses end cell end table

Ambil salah satu komponen kesamaan yang seletak:

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 6 plus open parentheses negative 2 x close parentheses end cell equals 0 row cell negative 2 x end cell equals 6 row x equals cell fraction numerator 6 over denominator negative 2 end fraction end cell row x equals cell negative 3 end cell end table

Dengan demikian, nilai x adalah negative 3.

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