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: negative 3 a with rightwards arrow on top plus 2 b with rightwards arrow on top.space 

 

Pembahasan Soal:

Jika terdapat 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 topb 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, dan skalar m, maka rumus penjumlahan vektor 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

dan rumus perkalian vektor dengan skalar adalah 

m a with rightwards arrow on top equals m x subscript 1 i with rightwards arrow on top plus m x subscript 2 j with rightwards arrow on top plus m x subscript 3 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 negative 3 a with rightwards arrow on top plus 2 b with rightwards arrow on top end cell equals cell negative 3 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 2 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 negative 9 i with rightwards arrow on top plus 6 j with rightwards arrow on top plus open parentheses negative 3 close parentheses k with rightwards arrow on top close parentheses plus open parentheses 2 i with rightwards arrow on top plus 6 j with rightwards arrow on top plus open parentheses negative 4 close parentheses k with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses negative 9 plus 2 close parentheses i with rightwards arrow on top plus open parentheses 6 plus 6 close parentheses j with rightwards arrow on top plus open parentheses negative 3 plus open parentheses negative 4 close parentheses close parentheses k with rightwards arrow on top end cell row blank equals cell open parentheses negative 7 close parentheses i with rightwards arrow on top plus open parentheses 12 close parentheses j with rightwards arrow on top plus open parentheses negative 7 close parentheses k with rightwards arrow on top end cell row blank equals cell negative 7 i with rightwards arrow on top plus 12 j with rightwards arrow on top plus negative 7 k with rightwards arrow on top end cell end table

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row cell negative 3 a with rightwards arrow on top plus 2 b with rightwards arrow on top end cell equals cell negative 7 i with rightwards arrow on top plus 12 j with rightwards arrow on top plus negative 7 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-vektor , , dan . Hasil dari adalah ...

Pembahasan Soal:

Diketahui bahwa vektor u with rightwards arrow on top, v with rightwards arrow on top, dan w with rightwards arrow on top merupakan vektor basis left parenthesis i comma j comma k right parenthesis spaceyang berada pada dimensi tiga yang dapat diubah ke vektor baris berada pada dimensi tiga sehingga diperoleh

u with rightwards arrow on top equals 2 i with rightwards arrow on top plus 3 j with rightwards arrow on top plus k with rightwards arrow on top ⟶ u with rightwards arrow on top equals open parentheses 2 , 3 comma 1 close parentheses  v with rightwards arrow on top equals 2 i with rightwards arrow on top plus 4 j with rightwards arrow on top plus k with rightwards arrow on top ⟶ v with rightwards arrow on top equals left parenthesis 2 , 4 comma 1 right parenthesis  w with rightwards arrow on top equals 2 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus 4 k with rightwards arrow on top ⟶ w with rightwards arrow on top equals open parentheses 2 comma negative 3 , 4 close parentheses

maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 u with rightwards arrow on top minus open parentheses 3 v with rightwards arrow on top minus w with rightwards arrow on top close parentheses end cell equals cell 4 open parentheses 2 , 3 comma 1 close parentheses minus left parenthesis 3 left parenthesis 2 , 4 comma 1 right parenthesis minus open parentheses 2 comma negative 3 , 4 close parentheses right parenthesis end cell row blank equals cell open parentheses 8 , 12 , 4 close parentheses plus left parenthesis open parentheses 6 , 12 , 3 close parentheses minus open parentheses 2 comma negative 3 , 4 close parentheses right parenthesis end cell row blank equals cell open parentheses 8 , 12 , 4 close parentheses plus open parentheses 4 , 15 comma negative 1 close parentheses end cell row blank equals cell open parentheses 4 comma negative 3 , 5 close parentheses end cell row blank equals cell 4 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus 5 k with rightwards arrow on top end cell end table

Jadi, hasil dari a with rightwards arrow on top plus 1 half b with rightwards arrow on top minus c with rightwards arrow on top adalah 4 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus 5 k with rightwards arrow on top.

Oleh karena itu, jawaban yang benar adalah C.

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Diketahui vektor a=(5−8​),b=(−43​)danc=(612​). Jika d=2a−b+61​c, maka vektor d=...

Pembahasan Soal:

Diketahui vektor

abc===(58)(43)(612)

Vektor d adalah hasil dari operasi hitung ketiga vektor di atas, maka

d======2ab+61c2(58)(43)+61(612)(2(5)2(8))(43)+(61(6)61(12))(1016)(43)+(12)(10(4)+1163+2)(1517)

Dengan demikian, vektor d=(1517).

Oleh karena itu, jawaban yang benar adalah B.

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Diketahui ; ; . Hasil dari

Pembahasan Soal:

Ingat! operasi penjumlahan, pengurangan serta perkalian vektor dengan skalar berikut ini:

open parentheses a top enclose i plus b top enclose j plus c top enclose k close parentheses plus-or-minus open parentheses x top enclose i plus y top enclose j plus z top enclose k close parentheses equals open parentheses a plus x close parentheses top enclose i plus-or-minus open parentheses b plus y close parentheses top enclose i plus-or-minus open parentheses c plus z close parentheses top enclose k

dan

p open parentheses a top enclose i plus b top enclose j plus c top enclose k close parentheses equals p a top enclose i plus p b top enclose j plus p c top enclose k 

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose a end cell equals cell 3 top enclose i plus 4 top enclose j minus 5 top enclose k end cell row cell top enclose b end cell equals cell 2 top enclose i minus 6 top enclose j plus 4 top enclose k end cell row cell top enclose c end cell equals cell 5 top enclose i plus 3 top enclose j minus 3 top enclose k end cell end table

Perhatikan perhitungan berikut ini:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose a plus 2 top enclose b minus 3 top enclose c end cell equals cell open parentheses 3 top enclose i plus 4 top enclose j minus 5 top enclose k close parentheses plus 2 open parentheses 2 top enclose i minus 6 top enclose j plus 4 top enclose k close parentheses minus 3 open parentheses 5 top enclose i plus 3 top enclose j minus 3 top enclose k close parentheses end cell row blank equals cell open parentheses 3 top enclose i plus 4 top enclose j minus 5 top enclose k close parentheses plus open parentheses 4 top enclose i minus 12 top enclose j plus 8 top enclose k close parentheses minus open parentheses 15 top enclose i plus 9 top enclose j minus 9 top enclose k close parentheses end cell row blank equals cell open parentheses 3 plus 4 minus 15 close parentheses top enclose i plus open parentheses 4 minus 12 minus 9 close parentheses top enclose j plus open parentheses negative 5 plus 8 minus open parentheses negative 9 close parentheses close parentheses top enclose k end cell row blank equals cell negative 8 top enclose i minus 17 top enclose j plus 12 top enclose k end cell end table end style

Dengan demikian table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell top enclose a 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 top enclose b 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 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell top enclose c end cell end table adalah 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 8 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell top enclose i 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 17 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell top enclose j 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 12 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell top enclose k end cell end table.

Oleh karena itu, jawaban yang benar adalah A.

0

Roboguru

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

Pembahasan Soal:

Dengan menyubtitusikan a with rightwards arrow on top equals open parentheses table row 3 row cell negative 1 end cell row 2 end table close parenthesesb with rightwards arrow on top equals open parentheses table row 4 row 1 row 0 end table close parentheses, dan c with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row 2 row 1 end table close parentheses ke 2 a with rightwards arrow on top minus 3 b with rightwards arrow on top plus k c with rightwards arrow on top equals open parentheses table row cell negative 7 end cell row cell negative 3 end cell row 5 end table close parentheses, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a with rightwards arrow on top minus 3 b with rightwards arrow on top plus k c with rightwards arrow on top end cell equals cell open parentheses table row cell negative 7 end cell row cell negative 3 end cell row 5 end table close parentheses end cell row cell 2 open parentheses table row 3 row cell negative 1 end cell row 2 end table close parentheses minus 3 open parentheses table row 4 row 1 row 0 end table close parentheses plus k open parentheses table row cell negative 1 end cell row 2 row 1 end table close parentheses end cell equals cell open parentheses table row cell negative 7 end cell row cell negative 3 end cell row 5 end table close parentheses end cell row cell open parentheses table row 6 row cell negative 2 end cell row 4 end table close parentheses minus open parentheses table row 12 row 3 row 0 end table close parentheses plus k open parentheses table row cell negative 1 end cell row 2 row 1 end table close parentheses end cell equals cell open parentheses table row cell negative 7 end cell row cell negative 3 end cell row 5 end table close parentheses end cell row cell open parentheses table row cell negative 6 end cell row cell negative 5 end cell row 4 end table close parentheses plus k open parentheses table row cell negative 1 end cell row 2 row 1 end table close parentheses end cell equals cell open parentheses table row cell negative 7 end cell row cell negative 3 end cell row 5 end table close parentheses end cell row cell k open parentheses table row cell negative 1 end cell row 2 row 1 end table close parentheses end cell equals cell open parentheses table row cell negative 7 end cell row cell negative 3 end cell row 5 end table close parentheses minus open parentheses table row cell negative 6 end cell row cell negative 5 end cell row 4 end table close parentheses end cell row cell k open parentheses table row cell negative 1 end cell row 2 row 1 end table close parentheses end cell equals cell open parentheses table row cell negative 7 plus 6 end cell row cell negative 3 plus 5 end cell row cell 5 minus 4 end cell end table close parentheses end cell row cell k open parentheses table row cell negative 1 end cell row 2 row 1 end table close parentheses end cell equals cell open parentheses table row cell negative 1 end cell row 2 row 1 end table close parentheses end cell row k equals 1 end table 

Jadi, nilai k adalah 1.space 

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Roboguru

Diketahui vektor , vektor , dan vektor . Tentukan !

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell p with rightwards arrow on top plus 2 q with rightwards arrow on top minus 3 r with rightwards arrow on top end cell equals cell open parentheses table row 3 row 4 end table close parentheses plus 2 open parentheses table row 5 row cell negative 1 end cell end table close parentheses minus 3 open parentheses table row cell negative 2 end cell row 6 end table close parentheses end cell row blank equals cell open parentheses table row 3 row 4 end table close parentheses plus open parentheses table row 10 row cell negative 2 end cell end table close parentheses minus open parentheses table row cell negative 6 end cell row 18 end table close parentheses end cell row blank equals cell open parentheses table row cell 3 plus 10 minus left parenthesis negative 6 right parenthesis end cell row cell 4 plus left parenthesis negative 2 right parenthesis minus 18 end cell end table close parentheses end cell row blank equals cell open parentheses table row 19 row cell negative 16 end cell end table close parentheses end cell end table 

Jadi p with rightwards arrow on top plus 2 q with rightwards arrow on top minus 3 r with rightwards arrow on top equals open parentheses table row 19 row cell negative 16 end cell end table close parentheses.

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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