Roboguru

Diketahui  dan . Tentukanlah: c.

Pertanyaan

Diketahui straight a with rightwards arrow on top equals 3 straight i with rightwards arrow on top minus 2 straight j with rightwards arrow on top plus straight k with rightwards arrow on top dan straight b with rightwards arrow on top equals straight i with rightwards arrow on top plus 3 straight j with rightwards arrow on top minus 2 straight k with rightwards arrow on top. Tentukanlah:

c. negative 3 straight a with rightwards arrow on top plus 2 straight b with rightwards arrow on top  

Pembahasan Soal:

Diketahui straight a with rightwards arrow on top equals 3 straight i with rightwards arrow on top minus 2 straight j with rightwards arrow on top plus straight k with rightwards arrow on top dan straight b with rightwards arrow on top equals straight i with rightwards arrow on top plus 3 straight j with rightwards arrow on top minus 2 straight k with rightwards arrow on top. Maka:

negative 3 straight a with rightwards arrow on top plus 2 straight b with rightwards arrow on top equals negative 3 open parentheses table row 3 row cell negative 2 end cell row 1 end table close parentheses plus 2 open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses minus 3 straight a with rightwards arrow on top plus 2 straight b with rightwards arrow on top equals open parentheses table row cell negative 9 end cell row 6 row cell negative 3 end cell end table close parentheses plus open parentheses table row 2 row 6 row cell negative 4 end cell end table close parentheses minus 3 straight a with rightwards arrow on top plus 2 straight b with rightwards arrow on top equals open parentheses table row cell negative 7 end cell row 12 row cell negative 7 end cell end table close parentheses 

Jadi, hasilnya adalah open parentheses table row cell negative 7 end cell row 12 row cell negative 7 end cell end table close parentheses.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

W. Lestari

Mahasiswa/Alumni Universitas Sriwijaya

Terakhir diupdate 06 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui vektor  dan . Panjang vektor

Pembahasan Soal:

Jika diketahui vektor u with rightwards arrow on top equals open parentheses table row x row y end table close parentheses, maka dapat ditentukan panjang vektor u with rightwards arrow on top sebagai berikut.

open vertical bar u with rightwards arrow on top close vertical bar equals square root of x squared plus y squared end root

Jika diketahui vektor u with rightwards arrow on top equals open parentheses table row x row y end table close parentheses dan v with rightwards arrow on top equals open parentheses table row a row b end table close parentheses, serta k element of R, maka dapat ditentukan operasi hitung sebagai berikut.

k times u with rightwards arrow on top equals k times 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

u with rightwards arrow on top plus v with rightwards arrow on top equals open parentheses table row x row y end table close parentheses plus open parentheses table row a row b end table close parentheses equals open parentheses table row cell x plus a end cell row cell y plus b end cell end table close parentheses

Dengan menerapkan operasi penjumlahan dua vektor dan perkalian skalar dengan vektor, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 u with rightwards arrow on top plus v with rightwards arrow on top end cell equals cell 2 open parentheses 4 i with hat on top plus 2 j with hat on top close parentheses plus open parentheses i with hat on top minus 2 j with hat on top close parentheses end cell row blank equals cell open parentheses 8 i with hat on top plus 4 j with hat on top close parentheses plus open parentheses i with hat on top minus 2 j with hat on top close parentheses end cell row blank equals cell 9 i with hat on top plus 2 j with hat on top end cell end table end style 

Dengan menerapkan rumus panjang vektor pada dua dimensi, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar 2 u with rightwards arrow on top plus v with rightwards arrow on top close vertical bar end cell equals cell square root of 9 squared plus 2 squared end root end cell row blank equals cell square root of 81 plus 4 end root end cell row blank equals cell square root of 85 end cell end table end style 

Dengan demikian, panjang vektor begin mathsize 14px style 2 u with rightwards arrow on top plus v with rightwards arrow on top end style adalah begin mathsize 14px style square root of 85 end style satuan.

1

Roboguru

Diketahui , ,  dan . Tentukan nilai !

Pembahasan Soal:

Diberikan vektor a with rightwards arrow on top equals negative i with rightwards arrow on top plus j with rightwards arrow on top minus k with rightwards arrow on top,  b with rightwards arrow on top equals i with rightwards arrow on top minus 2 j with rightwards arrow on top plus k with rightwards arrow on topc with rightwards arrow on top equals negative 4 i with rightwards arrow on top plus x k with rightwards arrow on top dan persamaan a with rightwards arrow on top times open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses equals a with rightwards arrow on top times a with rightwards arrow on top.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses end cell equals cell a with rightwards arrow on top times a with rightwards arrow on top end cell row cell open parentheses table row 1 row 1 row cell negative 1 end cell end table close parentheses times open parentheses open parentheses table row 1 row cell negative 2 end cell row 1 end table close parentheses plus open parentheses table row cell negative 4 end cell row 0 row x end table close parentheses close parentheses end cell equals cell open parentheses table row 1 row 1 row cell negative 1 end cell end table close parentheses times open parentheses table row 1 row 1 row cell negative 1 end cell end table close parentheses end cell row cell open parentheses table row 1 row 1 row cell negative 1 end cell end table close parentheses times open parentheses table row cell negative 3 end cell row cell negative 2 end cell row cell 1 plus x end cell end table close parentheses end cell equals cell open parentheses table row 1 row 1 row cell negative 1 end cell end table close parentheses times open parentheses table row 1 row 1 row cell negative 1 end cell end table close parentheses end cell row cell negative 3 minus 2 minus left parenthesis 1 plus x right parenthesis end cell equals cell 1 plus 1 plus 1 end cell row cell negative 5 minus 1 minus x end cell equals 3 row cell negative 6 minus x end cell equals 3 row cell negative x end cell equals cell 3 plus 6 end cell row cell negative x end cell equals 9 row x equals cell negative 9 end cell end table 

Jadi, nilai x adalah negative 9.

0

Roboguru

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

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.

1

Roboguru

Diketahui vektor  dan . Tentukan .

Pembahasan Soal:

Inget kembali perkalian vektor dengan skalar berikut ini.

k times open parentheses table row cell a subscript 1 end cell row cell a subscript 3 end cell row cell a subscript 3 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 row cell k a subscript 3 end cell end table close parentheses

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 row cell a subscript 3 plus b subscript 3 end cell end table close parentheses 

Oleh karena itu, kita peroleh hasil berikut ini.

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 1 half u with rightwards arrow on top plus 2 v with rightwards arrow on top end cell equals cell negative 1 half open parentheses table row cell negative 4 end cell row 8 row 2 end table close parentheses plus 2 open parentheses table row 5 row 1 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell negative 4 end cell row cell negative 1 end cell end table close parentheses plus open parentheses table row 10 row 2 row cell negative 8 end cell end table close parentheses end cell row blank blank blank row blank equals cell open parentheses table row 12 row cell negative 2 end cell row cell negative 9 end cell end table close parentheses end cell end table   

Jadi,table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell u with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell v 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 table row cell open parentheses table row 12 row cell negative 2 end cell row cell negative 9 end cell end table close parentheses end cell end table end cell end table 

0

Roboguru

Diketahui vektor  tegak lurus dengan vektor . Jika  maka

Pembahasan Soal:

Jika vektor a with rightwards arrow on top equals a subscript 1 i with rightwards arrow on top plus a subscript 2 j with rightwards arrow on top plus a subscript 3 k with rightwards arrow on top dan b with rightwards arrow on top equals b subscript 1 i with rightwards arrow on top plus b subscript 2 j with rightwards arrow on top plus b subscript 3 k with rightwards arrow on top, maka

a with rightwards arrow on top times b with rightwards arrow on top equals a subscript 1 times b subscript 1 plus a subscript 2 times b subscript 2 plus a subscript 3 times b subscript 3

Jika vektor a with rightwards arrow on top tegak lurus vektor b with rightwards arrow on top, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar space cos space alpha end cell row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals 0 end table

Berdasarkan konsep di atas, nilai x dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals 0 row cell open parentheses table row 2 row 3 row x end table close parentheses open parentheses table row 3 row cell negative 6 end cell row 2 end table close parentheses end cell equals 0 row cell 2 times 3 plus 3 open parentheses negative 6 close parentheses plus 2 x end cell equals 0 row cell 6 minus 18 plus 2 x end cell equals 0 row cell negative 12 plus 2 x end cell equals 0 row cell 2 x end cell equals 12 row x equals 6 end table

Diperoleh vektor x equals 6 sehingga a with rightwards arrow on top equals 2 i with rightwards arrow on top plus 3 j with rightwards arrow on top plus 6 k with rightwards arrow on top dan c with rightwards arrow on top equals 6 i with rightwards arrow on top minus 5 j with rightwards arrow on top plus k with rightwards arrow on top. Dapat ditentukan operasi penjumlahan dan pengurangan vektor berikut.

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

Diperoleh table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell b with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell c 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 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell i with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell j with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell k with rightwards arrow on top end cell end table

Oleh karena itu, jawaban yang tepat adalah B.

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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