Roboguru

Pertanyaan

Diketahui dua vektor a with bar on top equals open parentheses table row 1 row cell negative 1 end cell end table close parentheses dan b with bar on top equals open parentheses table row 3 row cell negative 4 end cell end table close parentheses. Tentukan nilai dari:

a. a with bar on top plus b with bar on top

b. a with bar on top plus 2 b with bar on top 

c. 3 a with bar on top minus 2 b with bar on top

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

diperoleh a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses table row 4 row cell negative 5 end cell end table close parenthesestable attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top plus 2 b with rightwards arrow on top end cell equals cell open parentheses table row 7 row cell negative 9 end cell end table close parentheses end cell end table, dan table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a with rightwards arrow on top minus 2 b with rightwards arrow on top end cell equals cell open parentheses table row cell negative 3 end cell row 5 end table close parentheses end cell end table.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses table row 4 row cell negative 5 end cell end table close parenthesestable attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top plus 2 b with rightwards arrow on top end cell equals cell open parentheses table row 7 row cell negative 9 end cell end table close parentheses end cell end table, dan table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a with rightwards arrow on top minus 2 b with rightwards arrow on top end cell equals cell open parentheses table row cell negative 3 end cell row 5 end table close parentheses end cell end table.

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. Penjumlahan dan pengurangan dua vektor tersebut dapat dirumuskan sebagai berikut.

a with rightwards arrow on top plus b 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

a with rightwards arrow on top minus b 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

Misalkan m adalah suatu skalar, hasil kali skalar m dengan 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 dapat ditentukan oleh rumus berikut.

m a 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

a. Hasil dari a with rightwards arrow on top plus b with rightwards arrow on top adalah sebagai berikut.

a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses table row 1 row cell negative 1 end cell end table close parentheses plus open parentheses table row 3 row cell negative 4 end cell end table close parentheses equals open parentheses table row 4 row cell negative 5 end cell end table close parentheses

b. Hasil dari a with rightwards arrow on top plus 2 b with rightwards arrow on top adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top plus 2 b with rightwards arrow on top end cell equals cell open parentheses table row 1 row cell negative 1 end cell end table close parentheses plus 2 open parentheses table row 3 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 1 row cell negative 1 end cell end table close parentheses plus open parentheses table row 6 row cell negative 8 end cell end table close parentheses end cell row blank equals cell open parentheses table row 7 row cell negative 9 end cell end table close parentheses end cell end table

c. Hasil dari 3 a with rightwards arrow on top minus 2 b with rightwards arrow on top adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a with rightwards arrow on top minus 2 b with rightwards arrow on top end cell equals cell 3 open parentheses table row 1 row cell negative 1 end cell end table close parentheses minus 2 open parentheses table row 3 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 3 row cell negative 3 end cell end table close parentheses minus open parentheses table row 6 row cell negative 8 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 end cell row 5 end table close parentheses end cell end table

Dengan demikian, diperoleh a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses table row 4 row cell negative 5 end cell end table close parenthesestable attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top plus 2 b with rightwards arrow on top end cell equals cell open parentheses table row 7 row cell negative 9 end cell end table close parentheses end cell end table, dan table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a with rightwards arrow on top minus 2 b with rightwards arrow on top end cell equals cell open parentheses table row cell negative 3 end cell row 5 end table close parentheses end cell end table.

7

5.0 (1 rating)

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