Roboguru

Diketahui vektor , dan . Tentukanlah: b.

Pertanyaan

Diketahui vektor straight a with rightwards arrow on top equals open parentheses table row 3 row cell negative 2 end cell row 1 end table close parentheses comma space straight b with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row 4 row 5 end table close parentheses, dan straight c with rightwards arrow on top equals open parentheses table row 5 row cell negative 3 end cell row 2 end table close parentheses. Tentukanlah:

b. 2 straight a with rightwards arrow on top plus 2 straight c with rightwards arrow on top  

Pembahasan Soal:

Diketahui vektor straight a with rightwards arrow on top equals open parentheses table row 3 row cell negative 2 end cell row 1 end table close parentheses comma space straight b with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row 4 row 5 end table close parentheses, dan straight c with rightwards arrow on top equals open parentheses table row 5 row cell negative 3 end cell row 2 end table close parentheses. Maka:

2 straight a with rightwards arrow on top plus 2 straight c with rightwards arrow on top equals 2 open parentheses table row 3 row cell negative 2 end cell row 1 end table close parentheses plus 2 open parentheses table row 5 row cell negative 3 end cell row 2 end table close parentheses 2 straight a with rightwards arrow on top plus 2 straight c with rightwards arrow on top equals open parentheses table row 6 row cell negative 4 end cell row 2 end table close parentheses plus open parentheses table row 10 row cell negative 6 end cell row 4 end table close parentheses 2 straight a with rightwards arrow on top plus 2 straight c with rightwards arrow on top equals open parentheses table row 16 row cell negative 10 end cell row 6 end table close parentheses  

Jadi, hasilnya adalah open parentheses table row 16 row cell negative 10 end cell row 6 end table close parentheses..

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

W. Lestari

Mahasiswa/Alumni Universitas Sriwijaya

Terakhir diupdate 06 Juni 2021

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Pertanyaan yang serupa

Tentukan panjang vektor dari , jika  dan

Pembahasan Soal:

Diketahui:

a with rightwards arrow on top equals open parentheses 2 comma negative 1 close parentheses

b with rightwards arrow on top equals open parentheses 1 comma negative 2 close parentheses

Ditanya:

panjang vektor dari a with rightwards arrow on top plus b with rightwards arrow on top=?

Jawab:

a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses table row 2 row cell negative 1 end cell end table close parentheses plus open parentheses table row 1 row cell negative 2 end cell end table close parentheses equals open parentheses table row 3 row cell negative 3 end cell end table close parentheses open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar equals square root of 3 squared plus open parentheses negative 3 close parentheses squared end root equals square root of 9 plus 9 end root equals square root of 18 equals 3 square root of 2 .

Jadi, panjang vektor dari a with rightwards arrow on top plus b with rightwards arrow on top adalah 3 square root of 2.

Jadi, jawaban yang tepat adalah B.

0

Roboguru

Diketahui vektor , , dan . Jika , nilai  adalah ...

Pembahasan Soal:

Permasalahan di atas dapat diselesaikan dengan kesamaan matriks.

Diketahui a with rightwards arrow on top equals open parentheses table row 4 row 2 end table close parentheses, b with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row cell negative 5 end cell end table close parentheses, dan c with rightwards arrow on top equals open parentheses table row cell negative 5 end cell row 1 end table close parentheses.

Jika x a with rightwards arrow on top plus y b with rightwards arrow on top equals c with rightwards arrow on top, maka:

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

Dari kesamaan matriks di atas diperoleh dua persamaan, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 x minus 3 y end cell equals cell negative 5 end cell row cell 2 x minus 5 y end cell equals 1 end table 

Eliminasi kedua persamaan untuk menentukan nilai y.

4 x minus 3 y equals negative 5 space open vertical bar times 1 close vertical bar space space space space 4 x minus 3 y equals negative 5 2 x minus 5 y equals 1 space space space space space open vertical bar times 2 close vertical bar space bottom enclose 4 x minus 10 y equals 2 space space space space space space end enclose space space minus space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 7 y equals negative 7 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space y equals fraction numerator negative 7 over denominator 7 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space y equals negative 1 

Substitusikan y equals negative 1 pada salah satu persamaan untuk menentukan nilai x.

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x minus 5 y end cell equals 1 row cell 2 x minus 5 open parentheses negative 1 close parentheses end cell equals 1 row cell 2 x plus 5 end cell equals 1 row cell 2 x end cell equals cell 1 minus 5 end cell row x equals cell fraction numerator negative 4 over denominator 2 end fraction end cell row x equals cell negative 2 end cell end table 

Nilai 5 x plus y squared adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 x plus y squared end cell equals cell 5 open parentheses negative 2 close parentheses plus open parentheses negative 1 close parentheses squared end cell row blank equals cell negative 10 plus 1 end cell row blank equals cell negative 9 end cell end table 

Sehingga, Error converting from MathML to accessible text..

Jadi, jawaban yang tepat adalah B.

0

Roboguru

Diketahui , dan . Jika  dan  memenuhi persamaan , berapa nilai dari  ?

Pembahasan Soal:

Diketahui straight a with rightwards arrow on top equals 2 straight i plus straight j comma space straight b with rightwards arrow on top equals straight i plus 3 straight j, dan straight c with rightwards arrow on top equals straight i minus 7 straight j. Jika straight m dan straight n memenuhi persamaan straight c with rightwards arrow on top equals straight m straight a with rightwards arrow on top plus straight n straight b with rightwards arrow on top, maka:

space space space space space space space space straight c with rightwards arrow on top equals straight m straight a with rightwards arrow on top plus straight n straight b with rightwards arrow on top open parentheses table row 1 row cell negative 7 end cell end table close parentheses equals straight m open parentheses table row 2 row 1 end table close parentheses plus straight n open parentheses table row 1 row 3 end table close parentheses open parentheses table row 1 row cell negative 7 end cell end table close parentheses equals open parentheses table row cell 2 straight m end cell row straight m end table close parentheses plus open parentheses table row straight n row cell 3 straight n end cell end table close parentheses open parentheses table row 1 row cell negative 7 end cell end table close parentheses equals open parentheses table row cell 2 straight m plus straight n end cell row cell straight m plus 3 straight n end cell end table close parentheses space rightwards arrow table row cell 2 straight m plus straight n equals 1 space... space open parentheses 1 close parentheses end cell row cell straight m plus 3 straight n equals negative 7 space... space open parentheses 2 close parentheses end cell end table 

Eliminasi (1) dan (2)

Error converting from MathML to accessible text. 

Subtitusi nilai text m end text ke (1)

space space 2 straight m plus straight n equals 1 2 open parentheses 2 close parentheses plus straight n equals 1 space space space space space 4 plus straight n equals 1 space space space space space space space space space space straight n equals 1 minus 4 space space space space space space space space space space straight n equals negative 3 

Sehingga:

straight m minus straight n equals 2 minus open parentheses negative 3 close parentheses equals 2 plus 3 equals 5 

Jadi, nilai dari open parentheses straight m minus straight n close parentheses adalah 5.

0

Roboguru

Diketahui a=3i−j​; b=2i+13j​ dan c=−2i−8j​. Tentukan: a. a+b dan ∣∣​a+b∣∣​

Pembahasan Soal:

Ingat!

Pada vektor, jika p=ai+bj dan q=ci+dj maka:

  • p+q=(ab)+(cd)=(a+cb+d) 
  • p=a2+b2 

Maka:

a+b====(31)+(213)(3+21+13)(512)5i+12j 

Sehingga:

a+b====52+12225+14416913satuanpanjang 

Dengan demikian, a+b=5i+12j dan a+b=13satuanpanjang.

0

Roboguru

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

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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