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adalah segienam beraturan dengan pusat . Jika  dan  masing-masing dinyatakan oleh vektor  dan , maka  adalah ....

Pertanyaan

ABCDEF adalah segienam beraturan dengan pusat straight O. Jika AB with rightwards arrow on top dan BC with rightwards arrow on top masing-masing dinyatakan oleh vektor straight u dan straight v, maka CD with rightwards arrow on top adalah ....

  1. straight u plus straight v 

  2. straight u minus straight v 

  3. 2 straight v minus straight u 

  4. straight u minus 2 straight v 

  5. straight v minus straight u 

Pembahasan Soal:

Dari informasi yang diberikan, dapat digambarkan menjadi:

Maka:

CD parallel to BO rightwards arrow CD equals BO BC parallel to AO rightwards arrow BC equals AO 

Sehingga:

BO equals BA plus AO CD equals BA plus BC CD equals negative AB plus BC CD equals negative straight u plus straight v CD equals straight v minus straight u 

Jadi, jawaban yang benar adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

W. Lestari

Mahasiswa/Alumni Universitas Sriwijaya

Terakhir diupdate 01 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui  dan  dengan  dan  konstanta serta vektor  dan  dua vektor tidak saling sejajar. Jika . Nilai  adalah ...

Pembahasan Soal:

Diketahui a with rightwards arrow on top equals 2 p with rightwards arrow on top plus q with rightwards arrow on top dan b with rightwards arrow on top equals p with rightwards arrow on top minus 4 q with rightwards arrow on top, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a with rightwards arrow on top minus 2 b with rightwards arrow on top end cell equals cell 2 open parentheses 2 p with rightwards arrow on top plus q with rightwards arrow on top close parentheses minus 2 open parentheses p with rightwards arrow on top minus 4 q with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses 4 p with rightwards arrow on top plus 2 q with rightwards arrow on top close parentheses minus open parentheses 2 p with rightwards arrow on top minus 8 q with rightwards arrow on top close parentheses end cell row blank equals cell 4 p with rightwards arrow on top minus 2 p with rightwards arrow on top plus 2 q with rightwards arrow on top plus 8 q with rightwards arrow on top end cell row blank equals cell 2 p with rightwards arrow on top plus 10 q with rightwards arrow on top space end cell end table

Diketahui pula c with rightwards arrow on top equals m p with rightwards arrow on top plus open parentheses m plus n minus 1 close parentheses q with rightwards arrow on top dan c with rightwards arrow on top equals 2 a with rightwards arrow on top minus 2 b with rightwards arrow on top, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell c with rightwards arrow on top end cell equals cell 2 a with rightwards arrow on top minus 2 b with rightwards arrow on top end cell row cell m p with rightwards arrow on top plus open parentheses m plus n minus 1 close parentheses q with rightwards arrow on top end cell equals cell 2 p with rightwards arrow on top plus 10 q with rightwards arrow on top space end cell row blank blank blank end table 

Dari kesamaan vektor tersebut diperoleh 

m equals 2 space dan space m plus n minus 1 equals 10 

Substitusi m equals 2 ke m plus n minus 1 equals 10, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell m plus n minus 1 end cell equals 10 row cell 2 plus n minus 1 end cell equals 10 row cell 1 plus n end cell equals 10 row n equals 9 end table 

Sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell m plus n end cell equals cell 2 plus 9 end cell row blank equals 11 end table 

Jadi, nilai open parentheses m plus n close parentheses adalah 9

0

Roboguru

Diketahui vektor  di . b. Jika . Tentukanlah .

Pembahasan Soal:

Ingat bentuk  left parenthesis a plus b right parenthesis squared equals left parenthesis a minus b right parenthesis squared plus 4 a b.

Sehingga didapat:

vertical line u with rightwards arrow on top plus v with rightwards arrow on top vertical line squared equals vertical line u with rightwards arrow on top minus v with rightwards arrow on top vertical line squared plus 4 vertical line u with rightwards arrow on top vertical line vertical line v with rightwards arrow on top vertical line vertical line u with rightwards arrow on top plus v with rightwards arrow on top vertical line squared equals open parentheses square root of 37 close parentheses squared plus 4 left parenthesis 4 right parenthesis left parenthesis 3 right parenthesis vertical line u with rightwards arrow on top plus v with rightwards arrow on top vertical line squared equals 37 plus 48 equals 85 space vertical line u with rightwards arrow on top plus v with rightwards arrow on top vertical line equals square root of 85 

Jadi, vertical line u with rightwards arrow on top plus v with rightwards arrow on top vertical line equals square root of 85.

0

Roboguru

Diketahui titik-titik: ,  dan . Jika ,  dan  secara berturut-turut menyatakan vektor posisi titik A, B dan C, maka panjang dari

Pembahasan Soal:

Diketahui titik-titik: straight A left parenthesis 4 comma space 5 right parenthesis, straight B left parenthesis negative 1 comma space 1 right parenthesis dan straight C left parenthesis 2 comma space 6 right parenthesis. Dapat ditulis dalam bentuk vektor posisi stack O A with rightwards arrow on top equals a with rightwards arrow on top equals open parentheses table row 4 row 5 end table close parenthesesstack O B with rightwards arrow on top equals b with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row 1 end table close parentheses dan stack O C with rightwards arrow on top equals c with rightwards arrow on top equals open parentheses table row 2 row 6 end table close parentheses.

Ingat!

  • Pada vektor, jika a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses dan b with rightwards arrow on top equals open parentheses table row cell b subscript 1 end cell row cell b 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 a subscript 1 plus b subscript 1 end cell row cell a subscript 2 plus b subscript 2 end cell end table close parentheses.
  • Jika vektor a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses atau a with rightwards arrow on top equals left parenthesis a subscript 1 comma space a subscript 2 right parenthesis maka panjang vektor a with rightwards arrow on top adalah open vertical bar a with rightwards arrow on top close vertical bar equals square root of a subscript 1 squared plus a subscript 2 squared end root.

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top plus b with rightwards arrow on top plus c with rightwards arrow on top end cell equals cell left parenthesis a with rightwards arrow on top plus b with rightwards arrow on top right parenthesis plus c with rightwards arrow on top end cell row blank equals cell open parentheses table row 4 row 5 end table close parentheses plus open parentheses table row cell negative 1 end cell row 1 end table close parentheses plus open parentheses table row 2 row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell 4 plus left parenthesis negative 1 right parenthesis end cell row cell 5 plus 1 end cell end table close parentheses plus open parentheses table row 2 row 6 end table close parentheses end cell row blank equals cell open parentheses table row 3 row 6 end table close parentheses plus open parentheses table row 2 row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell 3 plus 2 end cell row cell 6 plus 6 end cell end table close parentheses end cell row blank equals cell open parentheses table row 5 row 12 end table close parentheses end cell end table  

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top plus c with rightwards arrow on top close vertical bar end cell equals cell square root of 5 squared plus 12 squared end root end cell row blank equals cell square root of 25 plus 144 end root end cell row blank equals cell square root of 169 end cell row blank equals cell 13 space satuan space panjang end cell end table  

Jadi, jawaban yang tepat adalah D.

0

Roboguru

Diketahui ,  dan . Jika  maka nilai  sama dengan ...

Pembahasan Soal:

Diketahui a with bar on top equals open parentheses table row cell negative 3 end cell row 4 end table close parenthesesb with bar on top equals open parentheses table row 1 row cell negative 1 end cell end table close parentheses dan c with bar on top equals open parentheses table row cell negative 2 end cell row 1 end table close parentheses

Ingat!

  • Secara aljabar, perkalian vektor dengan skalar di R squared dapat dirumuskan dengan a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses maka k a with rightwards arrow on top equals k open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses equals open parentheses table row cell k a subscript 1 end cell row cell k a subscript 2 end cell end table close parentheses.
  • Pada vektor, jika a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses dan b with rightwards arrow on top equals open parentheses table row cell b subscript 1 end cell row cell b 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 a subscript 1 plus b subscript 1 end cell row cell a subscript 2 plus b subscript 2 end cell end table close parentheses.

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell x a with bar on top plus y b with bar on top end cell equals cell c with bar on top end cell row cell x open parentheses table row cell negative 3 end cell row 4 end table close parentheses plus y open parentheses table row 1 row cell negative 1 end cell end table close parentheses end cell equals cell open parentheses table row cell negative 2 end cell row 1 end table close parentheses end cell row cell open parentheses table row cell negative 3 x end cell row cell 4 x end cell end table close parentheses plus open parentheses table row y row cell negative y end cell end table close parentheses end cell equals cell open parentheses table row cell negative 2 end cell row 1 end table close parentheses end cell row cell open parentheses table row cell negative 3 x plus y end cell row cell 4 x minus y end cell end table close parentheses end cell equals cell open parentheses table row cell negative 2 end cell row 1 end table close parentheses end cell end table 

Dari kesamaan vektor di atas didapat:

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 3 x plus y end cell equals cell negative 2 space... space left parenthesis 1 right parenthesis end cell row cell 4 x minus y end cell equals cell 1 space...... space left parenthesis 2 right parenthesis end cell end table 

Dengan menggunakan metode eliminasi, maka:

table row cell negative 3 x plus y equals negative 2 end cell row cell 4 x minus y equals 1 space space space space space plus end cell row cell x equals negative 1 end cell end table

Kita sustitusikan x=-1 ke salah satu persamaan yaitu 4x-y=1, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 x minus y end cell equals 1 row cell 4 left parenthesis negative 1 right parenthesis minus y end cell equals 1 row cell negative 4 minus y end cell equals 1 row cell negative y end cell equals cell 1 plus 4 end cell row cell negative y end cell equals 5 row y equals cell negative 5 end cell end table  

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell x y end cell equals cell left parenthesis negative 1 right parenthesis cross times left parenthesis negative 5 right parenthesis end cell row blank equals 5 end table 

Jadi, jawaban yang tepat adalah E.

0

Roboguru

Jika vektor  dan . Tentukanlah: a.

Pembahasan Soal:

Vektor merupakan suatu besaran yang memiliki arah.

Diketahui:

begin mathsize 14px style m with rightwards arrow on top equals negative 2 i with rightwards arrow on top plus 3 j with rightwards arrow on top end style
begin mathsize 14px style n with rightwards arrow on top equals 5 i with rightwards arrow on top plus 2 j with rightwards arrow on top end style

Vektor begin mathsize 14px style 5 m with rightwards arrow on top plus 2 n with rightwards arrow on top end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 5 m with rightwards arrow on top plus 2 n with rightwards arrow on top end cell equals cell 5 open parentheses negative 2 i with rightwards arrow on top plus 3 j with rightwards arrow on top close parentheses plus 2 open parentheses 5 i with rightwards arrow on top plus 2 j with rightwards arrow on top close parentheses end cell row blank equals cell negative 10 i with rightwards arrow on top plus 15 j with rightwards arrow on top plus 10 i with rightwards arrow on top plus 4 j with rightwards arrow on top end cell row blank equals cell negative 10 i with rightwards arrow on top plus 10 i with rightwards arrow on top plus 15 j with rightwards arrow on top plus 4 j with rightwards arrow on top end cell row blank equals cell 19 j with rightwards arrow on top end cell end table end style 

Jadi, nilai vektor begin mathsize 14px style 5 m with rightwards arrow on top plus 2 n with rightwards arrow on top end style adalah begin mathsize 14px style 19 j with rightwards arrow on top end style

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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