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Diketahui vektor u=(−85​), vektor v=(−1−4​), dan vektor w=(39​). Tentukan:         a.  2u+3v

Pertanyaan

Diketahui vektor u with rightwards arrow on top equals open parentheses table row cell negative 8 end cell row 5 end table close parentheses, vektor v with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row cell negative 4 end cell end table close parentheses, dan vektor w with rightwards arrow on top equals open parentheses table row 3 row 9 end table close parentheses. Tentukan:

        a.  2 u with rightwards arrow on top plus 3 v with rightwards arrow on top

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Jawaban terverifikasi

Jawaban

hasil dari 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative 19 end cell row cell negative 2 end cell 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 blank blank cell open parentheses table row cell bold minus bold 19 end cell row cell bold minus bold 2 end cell end table close parentheses end cell end table.

Ingat!

  • Rumus penjumlahan dua vektor jika diketahui a with rightwards arrow on top equals open parentheses table row cell x subscript 1 end cell row cell y subscript 1 end cell end table close parentheses dan vektor b with rightwards arrow on top equals open parentheses table row cell x subscript 2 end cell row cell y subscript 2 end cell end table close parentheses maka 

a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses table row cell x subscript 1 end cell row cell y subscript 1 end cell end table close parentheses plus open parentheses table row cell x subscript 2 end cell row cell y subscript 2 end cell end table close parentheses equals open parentheses table row cell x subscript 1 plus x subscript 2 end cell row cell y subscript 1 plus y subscript 2 end cell end table close parentheses 

  • Rumus untuk perkalian skalar m dengan vektor a with rightwards arrow on top equals open parentheses table row cell x subscript 1 end cell row cell y subscript 1 end cell end table close parentheses adalah sebagai berikut:

m a with rightwards arrow on top equals m open parentheses table row cell x subscript 1 end cell row cell x subscript 2 end cell end table close parentheses equals open parentheses table row cell m x subscript 1 end cell row cell m x subscript 2 end cell end table close parentheses

Diketahui:

Vektor u with rightwards arrow on top equals open parentheses table row cell negative 8 end cell row 5 end table close parentheses

Vektor v with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row cell negative 4 end cell end table close parentheses

Vektor w with rightwards arrow on top equals open parentheses table row 3 row 9 end table close parentheses.

Ditanya: 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top.

Dengan menggunakan rumus-rumus di atas, maka 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top adalah sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top end cell equals cell 2 open parentheses table row cell negative 8 end cell row 5 end table close parentheses plus 3 open parentheses table row cell negative 1 end cell row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 16 end cell row 10 end table close parentheses plus open parentheses table row cell negative 3 end cell row cell negative 12 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 16 minus 3 end cell row cell 10 minus 12 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 19 end cell row cell negative 2 end cell end table close parentheses end cell end table 

Dengan demikian, hasil dari 2 u with rightwards arrow on top plus 3 v with rightwards arrow on top adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative 19 end cell row cell negative 2 end cell end table close parentheses end cell end table.

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