Roboguru

Diketahui  dan . Tentukanlah: .

Pertanyaan

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

Tentukanlah: a with rightwards arrow on top plus b with rightwards arrow on top.space 

 

Pembahasan Soal:

Rumus penjumlahan vektor a with rightwards arrow on top equals x subscript 1 i with rightwards arrow on top plus x subscript 2 j with rightwards arrow on top plus x subscript 3 k with rightwards arrow on top dan b with rightwards arrow on top equals y subscript 1 i with rightwards arrow on top plus y subscript 2 j with rightwards arrow on top plus y subscript 3 k with rightwards arrow on top adalah 

a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses x subscript 1 plus y subscript 1 close parentheses i with rightwards arrow on top plus open parentheses x subscript 2 plus y subscript 2 close parentheses j with rightwards arrow on top plus open parentheses x subscript 3 plus y subscript 3 close parentheses k with rightwards arrow on top

Dengan menyelesaikan permasalahan pada soal,

a with rightwards arrow on top equals 3 i with rightwards arrow on top minus 2 j with rightwards arrow on top plus k with rightwards arrow on top equals 3 i with rightwards arrow on top plus open parentheses negative 2 close parentheses j with rightwards arrow on top plus k with rightwards arrow on top
b with rightwards arrow on top equals i with rightwards arrow on top plus 3 j with rightwards arrow on top minus 2 k with rightwards arrow on top equals i with rightwards arrow on top plus 3 j with rightwards arrow on top plus open parentheses negative 2 close parentheses k with rightwards arrow on top 

menggunakan rumus di atas, diperoleh

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 end cell equals cell open parentheses 3 i with rightwards arrow on top plus open parentheses negative 2 close parentheses j with rightwards arrow on top plus k with rightwards arrow on top close parentheses plus open parentheses i with rightwards arrow on top plus 3 j with rightwards arrow on top plus open parentheses negative 2 close parentheses k with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses 3 plus 1 close parentheses i with rightwards arrow on top plus open parentheses negative 2 plus 3 close parentheses j with rightwards arrow on top plus open parentheses 1 plus open parentheses negative 2 close parentheses close parentheses k with rightwards arrow on top end cell row blank equals cell open parentheses 4 close parentheses i with rightwards arrow on top plus open parentheses 1 close parentheses j with rightwards arrow on top plus open parentheses negative 1 close parentheses k with rightwards arrow on top end cell row blank equals cell 4 i with rightwards arrow on top plus j with rightwards arrow on top minus 1 k with rightwards arrow on top end cell end table 

Jadi, 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 end cell equals cell 4 i with rightwards arrow on top plus j with rightwards arrow on top minus 1 k with rightwards arrow on top end cell end table.space 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Ridha

Mahasiswa/Alumni Universitas Negeri Surabaya

Terakhir diupdate 05 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui vektor  dan . Jika , nilai  adalah ...

Pembahasan Soal:

Berdasarkan konsep penjumlahan vektor pada dua dimensi maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight w with rightwards arrow on top end cell equals cell 2 straight u with rightwards arrow on top plus 3 straight v with rightwards arrow on top end cell row blank equals cell 2 open parentheses table row cell negative 4 end cell row cell negative 2 end cell end table close parentheses plus 3 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 cell negative 8 end cell row cell negative 4 end cell end table close parentheses plus open parentheses table row cell negative 3 end cell row 15 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 11 end cell row 11 end table close parentheses end cell end table 

sehingga nilai open vertical bar straight w with rightwards arrow on top close vertical bar adalah panjang vektor straight w with rightwards arrow on top maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight w with rightwards arrow on top end cell equals cell square root of open parentheses negative 11 close parentheses squared plus 11 squared end root end cell row blank equals cell square root of 121 plus 121 end root end cell row blank equals cell square root of 121 cross times 2 end root end cell row blank equals cell 11 square root of 2 end cell end table 

Oleh karena itu, jawaban yang benar adalah E.

0

Roboguru

Diketahui vektor-vektor , , dan . Hasil dari  adalah ...

Pembahasan Soal:

Kita ingat operasi pada vektor.

3 p with rightwards arrow on top minus q with rightwards arrow on top plus 2 r with rightwards arrow on top equals 3 open parentheses table row 10 row cell negative 3 end cell row 0 end table close parentheses minus open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses plus 2 open parentheses table row 0 row 4 row 7 end table close parentheses space space space space space space space space space space space space space space space space space space space equals open parentheses table row 30 row cell negative 9 end cell row 0 end table close parentheses minus open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses plus open parentheses table row 0 row 8 row 14 end table close parentheses space space space space space space space space space space space space space space space space space space space equals open parentheses table row 27 row cell negative 3 end cell row 15 end table close parentheses 

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Perhatikan gambar berikut. Pernyataan yang benar adalah ....

Pembahasan Soal:

Perhatikan gambar dibawah ini.



Berdasarkan cara tersebut, maka diperoleh:

begin mathsize 14px style u with rightwards arrow on top equals v with rightwards arrow on top plus w with rightwards arrow on top v with rightwards arrow on top plus w with rightwards arrow on top minus u with rightwards arrow on top equals 0 end style 

Tidak ada pilihan jawaban yang benar. Jjawaban yang benar adalah begin mathsize 14px style v with rightwards arrow on top plus w with rightwards arrow on top minus u with rightwards arrow on top equals 0 end style.

0

Roboguru

Hasil operasi vektor  adalah ...

Pembahasan Soal:

Operasi tersebut adalah penjumlahan dan pengurangan vektor.

open parentheses table row cell negative 4 end cell row 7 end table close parentheses minus open parentheses table row cell negative 3 end cell row cell negative 5 end cell end table close parentheses plus open parentheses table row cell negative 6 end cell row 2 end table close parentheses equals open parentheses table row cell negative 7 end cell row 14 end table close parentheses

Sehingga, open parentheses table row cell negative 4 end cell row 7 end table close parentheses minus open parentheses table row cell negative 3 end cell row cell negative 5 end cell end table close parentheses plus open parentheses table row cell negative 6 end cell row 2 end table close parentheses equals open parentheses table row cell negative 7 end cell row 14 end table close parentheses.

Jadi, pilihan jawaban yang tepat adalah B.

0

Roboguru

Diketahui vektor , , dan . Hasil dari  adalah ...

Pembahasan Soal:

Ingat!

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell open parentheses table row p row q row r end table close parentheses end cell row cell k times a with rightwards arrow on top end cell equals cell open parentheses table row cell k times p end cell row cell k times q end cell row cell k times r end cell end table close parentheses end cell end table 

Diketahui a with rightwards arrow on top equals open parentheses table row 1 row 2 row 3 end table close parentheses, b with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row cell negative 2 end cell row cell negative 1 end cell end table close parentheses, dan c with rightwards arrow on top equals open parentheses table row 1 row cell negative 2 end cell row 3 end table close parentheses, maka hasil dari 2 a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top adalah:

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

Sehingga, 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 a 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 b 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 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 cell open parentheses table row cell negative 2 end cell row 4 row 2 end table close parentheses end cell end table.

Jadi, 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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