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Jika . Tentukan hasil dari  !

Pertanyaan

Jika a with rightwards arrow on top equals open parentheses table row cell negative 8 end cell row 4 row cell negative 2 end cell end table close parentheses. Tentukan hasil dari 4 a with rightwards arrow on top !

Pembahasan Soal:

Operasi perkalian vektor dengan skalar dapat dihitung seperti berikut,

4 a with rightwards arrow on top equals 4 times open parentheses table row cell negative 8 end cell row 4 row cell negative 2 end cell end table close parentheses equals open parentheses table row cell negative 32 end cell row 16 row cell negative 8 end cell end table close parentheses 

Jadi, hasil operasi vektor di atas adalah open parentheses table row cell negative 32 end cell row 16 row cell negative 8 end cell end table close parentheses.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Kumaralalita

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 01 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika vektor  dan , vektor  yang memenuhi operasi  adalah ...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 v with rightwards arrow on top plus 2 w with rightwards arrow on top end cell equals cell u with rightwards arrow on top minus v with rightwards arrow on top end cell row cell 2 w with rightwards arrow on top end cell equals cell u with rightwards arrow on top minus 4 v with rightwards arrow on top end cell row cell 2 w with rightwards arrow on top end cell equals cell open parentheses table row 4 row 6 end table close parentheses minus 4 open parentheses table row 3 row cell negative 1 end cell end table close parentheses end cell row cell 2 w with rightwards arrow on top end cell equals cell open parentheses table row cell 4 minus 4 times 3 end cell row cell 6 minus 4 times open parentheses negative 1 close parentheses end cell end table close parentheses end cell row cell 2 w with rightwards arrow on top end cell equals cell open parentheses table row cell negative 8 end cell row 10 end table close parentheses end cell row cell w with rightwards arrow on top end cell equals cell 1 half open parentheses table row cell negative 8 end cell row 10 end table close parentheses end cell row cell w with rightwards arrow on top end cell equals cell open parentheses table row cell negative 4 end cell row 5 end table close parentheses end cell end table end style 

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Jika  dan , tentukan vektor-vektor berikut dan hitung juga besarnya. a.

Pembahasan Soal:

Jika sebuah vektor dikalikan dengan skalar, maka masing-masing elemen vektor tersebut dikalikan dengan skalar. Sehingga, 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 bold italic p end cell equals cell 4 times open parentheses table row cell negative 5 end cell row 12 end table close parentheses end cell row blank equals cell open parentheses table row cell 4 times left parenthesis negative 5 right parenthesis end cell row cell 4 times 12 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 20 end cell row 48 end table close parentheses end cell end table end style 

Jadi, hasil dari Error converting from MathML to accessible text.adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative 20 end cell row 48 end table close parentheses end cell end table end style.

0

Roboguru

Jika . b. Tentukan

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a plus b end cell equals cell 2 open parentheses 2 comma space 3 comma space 4 close parentheses plus left parenthesis negative 2 comma space 1 comma space 3 right parenthesis end cell row blank equals cell left parenthesis 4 comma space 6 comma space 8 right parenthesis plus left parenthesis negative 2 comma space 1 comma space 3 right parenthesis end cell row blank equals cell left parenthesis 2 comma space 7 comma space 11 right parenthesis end cell row blank blank blank row cell vertical line 2 a plus b vertical line end cell equals cell square root of 2 squared plus 7 squared plus 11 squared end root end cell row blank equals cell square root of 4 plus 49 plus 121 end root end cell row blank equals cell square root of 174 end cell end table end style

0

Roboguru

Diketahui vektor , , dan  . Jika vektor  mewakili , vektor  mewakili , dan vektor  mewakili , tentukan !

Pembahasan Soal:

Dari soal yang diberikan, dapat diketahui:

OP with rightwards arrow on top equals straight p with rightwards arrow on top equals open parentheses table row 3 row cell negative 2 end cell end table close parentheses OQ with rightwards arrow on top equals straight q with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row 5 end table close parentheses OR with rightwards arrow on top equals straight r with rightwards arrow on top equals open parentheses table row 7 row 4 end table close parentheses 

Maka:

  • Menentukan vektor straight a with rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top end cell equals cell PQ with rightwards arrow on top end cell row blank equals cell straight q with rightwards arrow on top plus straight p with rightwards arrow on top end cell row blank equals cell open parentheses table row cell negative 1 end cell row 5 end table close parentheses minus open parentheses table row 3 row cell negative 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell row 7 end table close parentheses end cell end table 

  • Menentukan vektor straight b with rightwards arrow on top 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight b with rightwards arrow on top end cell equals cell QR with rightwards arrow on top end cell row blank equals cell straight r with rightwards arrow on top plus straight q with rightwards arrow on top end cell row blank equals cell open parentheses table row 7 row 4 end table close parentheses minus open parentheses table row cell negative 1 end cell row 5 end table close parentheses end cell row blank equals cell open parentheses table row 8 row cell negative 1 end cell end table close parentheses end cell end table 

  • Menentukan vektor straight c with rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row cell straight c with rightwards arrow on top end cell equals cell PR with rightwards arrow on top end cell row blank equals cell straight r with rightwards arrow on top plus straight p with rightwards arrow on top end cell row blank equals cell open parentheses table row 7 row 4 end table close parentheses minus open parentheses table row 3 row cell negative 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 4 row 6 end table close parentheses end cell end table 

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 straight c with rightwards arrow on top minus 4 straight b with rightwards arrow on top end cell equals cell 5 open parentheses table row 4 row 6 end table close parentheses minus 4 open parentheses table row 8 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 20 row 30 end table close parentheses minus open parentheses table row 32 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 12 end cell row 34 end table close parentheses end cell end table    

Jadi, 5 straight c with rightwards arrow on top minus 4 straight b with rightwards arrow on top equals open parentheses table row cell negative 12 end cell row 34 end table close parentheses.

0

Roboguru

Jika , dan , maka vektor adalah ...

Pembahasan Soal:

Misalkan terdapat vektor straight a with rightwards arrow on top equals open parentheses table row cell straight a subscript 1 end cell row cell straight a subscript 2 end cell end table close parentheses, straight b with rightwards arrow on top equals open parentheses table row cell straight b subscript 1 end cell row cell straight b subscript 2 end cell end table close parentheses dan straight k adalah skalar. maka berlaku:

open parentheses straight i close parentheses space straight a with rightwards arrow on top plus-or-minus straight b with rightwards arrow on top equals open parentheses table row cell straight a subscript 1 plus-or-minus straight b subscript 1 end cell row cell straight a subscript 2 plus-or-minus straight b subscript 2 end cell end table close parentheses left parenthesis ii right parenthesis space straight k straight a with rightwards arrow on top equals open parentheses table row cell ka subscript 1 end cell row cell ka subscript 2 end cell end table close parentheses

Berdasarkan sifat-sifat operasi vektor tersebut, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight d with rightwards arrow on top end cell equals cell straight a with rightwards arrow on top plus 3 straight b with rightwards arrow on top minus 2 straight c with rightwards arrow on top end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row 2 row cell negative 1 end cell end table close parentheses plus 3 open parentheses table row 4 row cell negative 2 end cell end table close parentheses minus 2 open parentheses table row cell negative 1 end cell row 3 end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row 2 row cell negative 1 end cell end table close parentheses plus open parentheses table row 12 row cell negative 6 end cell end table close parentheses minus open parentheses table row cell negative 2 end cell row 6 end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row cell 2 plus 12 plus 2 end cell row cell negative 1 minus 6 minus 6 end cell end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row 16 row cell negative 13 end cell end table close parentheses end cell end table

Dengan demikian, hasil operasi vektor pada soal adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight d with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 16 row cell negative 13 end cell end table close parentheses end cell end table.

Oleh karena itu, tidak ada jawaban yang benar.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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