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Diketahui vektor-vektor a=(34​), b=(8−6​), c=(−42​), d=(11​), dan e=(−55​),. Tentukan: g. b−c h. 2d−a

Pertanyaan

Diketahui vektor-vektor a with rightwards arrow on top equals open parentheses table row 3 row 4 end table close parentheses comma space b with rightwards arrow on top equals open parentheses table row 8 row cell negative 6 end cell end table close parentheses comma space c with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 2 end table close parentheses comma d with rightwards arrow on top equals open parentheses table row 1 row 1 end table close parentheses comma dan e with rightwards arrow on top equals open parentheses table row cell negative 5 end cell row 5 end table close parentheses comma. Tentukan:

g. b with rightwards arrow on top minus c with rightwards arrow on top

h. 2 d with rightwards arrow on top minus a with rightwards arrow on top

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

vektor hasil operasi b with rightwards arrow on top minus c with rightwards arrow on top dan 2 d with rightwards arrow on top minus a with rightwards arrow on top berturut-turut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 12 row cell negative 8 end cell end table close parentheses end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative 1 end cell row cell negative 2 end cell end table close parentheses end cell end table.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah g. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 12 row cell negative 8 end cell end table close parentheses end cell end table dan h. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative 1 end cell row cell negative 2 end cell end table close parentheses end cell end table.

Ingat

  • k open parentheses table row x row y end table close parentheses equals open parentheses table row cell k x end cell row cell k y end cell end table close parentheses comma space k equals skalar
  • 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 

Diketahui vektor-vektor a with rightwards arrow on top equals open parentheses table row 3 row 4 end table close parentheses comma space b with rightwards arrow on top equals open parentheses table row 8 row cell negative 6 end cell end table close parentheses comma space c with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 2 end table close parentheses comma d with rightwards arrow on top equals open parentheses table row 1 row 1 end table close parentheses comma dan e with rightwards arrow on top equals open parentheses table row cell negative 5 end cell row 5 end table close parentheses comma sehingga dapat ditentukan:

g. b with rightwards arrow on top minus c with rightwards arrow on top, menggunakan pengurangan vektor secara aljabar, didapatkan

table attributes columnalign right center left columnspacing 0px end attributes row cell b with rightwards arrow on top minus c with rightwards arrow on top end cell equals cell open parentheses table row 8 row cell negative 6 end cell end table close parentheses minus open parentheses table row cell negative 4 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell 8 minus open parentheses negative 4 close parentheses end cell row cell negative 6 minus 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 12 row cell negative 8 end cell end table close parentheses end cell end table

h. 2 d with rightwards arrow on top minus a with rightwards arrow on top, menggunakan perkalian vektor dengan skalar dan pengurangan vektor secara aljabar, didapatkan

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

Dengan demikian, vektor hasil operasi b with rightwards arrow on top minus c with rightwards arrow on top dan 2 d with rightwards arrow on top minus a with rightwards arrow on top berturut-turut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 12 row cell negative 8 end cell end table close parentheses end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative 1 end cell row cell negative 2 end cell end table close parentheses end cell end table.

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