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Diketahui dua vektor u=(−27​) dan v=(62​), tentukan! b. u+2v  c. 3u−2v

Pertanyaan

Diketahui dua vektor u with bar on top equals open parentheses table row cell negative 2 end cell row 7 end table close parentheses dan v with bar on top equals open parentheses table row 6 row 2 end table close parentheses, tentukan!

b. u with bar on top plus 2 v with bar on top 

c. 3 u with bar on top minus 2 v with bar on top

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

diperoleh table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top plus 2 v with rightwards arrow on top end cell equals cell open parentheses table row 10 row 11 end table close parentheses end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row cell 3 u with rightwards arrow on top minus 2 v with rightwards arrow on top end cell equals cell open parentheses table row cell negative 18 end cell row 17 end table close parentheses end cell end table.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top plus 2 v with rightwards arrow on top end cell equals cell open parentheses table row 10 row 11 end table close parentheses end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row cell 3 u with rightwards arrow on top minus 2 v with rightwards arrow on top end cell equals cell open parentheses table row cell negative 18 end cell row 17 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

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

table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top plus 2 v with rightwards arrow on top end cell equals cell open parentheses table row cell negative 2 end cell row 7 end table close parentheses plus 2 open parentheses table row 6 row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell row 7 end table close parentheses plus open parentheses table row 12 row 4 end table close parentheses end cell row blank equals cell open parentheses table row 10 row 11 end table close parentheses end cell end table

c. Hasil dari 3 u with rightwards arrow on top minus 2 v with rightwards arrow on top adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 u with rightwards arrow on top minus 2 v with rightwards arrow on top end cell equals cell 3 open parentheses table row cell negative 2 end cell row 7 end table close parentheses minus 2 open parentheses table row 6 row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 6 end cell row 21 end table close parentheses minus open parentheses table row 12 row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 18 end cell row 17 end table close parentheses end cell end table

Dengan demikian, diperoleh table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards arrow on top plus 2 v with rightwards arrow on top end cell equals cell open parentheses table row 10 row 11 end table close parentheses end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row cell 3 u with rightwards arrow on top minus 2 v with rightwards arrow on top end cell equals cell open parentheses table row cell negative 18 end cell row 17 end table close parentheses end cell end table.

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Diketahui dua vektor a=(1−1​) dan b=(3−4​). Tentukan nilai dari: a. a+b b. a+2b  c. 3a−2b

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