Roboguru

Diketahui vektor , , dan . Vektor yang mewakili  adalah ...

Pertanyaan

Diketahui vektor a with rightwards arrow on top equals 3 i minus 2 j plus kb with rightwards arrow on top equals 2 i minus 3 k, dan c with rightwards arrow on top equals j minus 2 k. Vektor yang mewakili 2 a with rightwards arrow on top minus 3 b with rightwards arrow on top plus c with rightwards arrow on top adalah ...

  1. 12 i minus 5 j plus 12 k 

  2. negative 3 j plus 9 k 

  3. negative 7 j minus 9 k 

  4. negative 3 i minus 3 j plus 9 k 

  5. 3 i minus j plus 9 k 

Pembahasan Soal:

Operasi hitung vektor tersebut dapat ditentukan sebagai berikut.

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 c with rightwards arrow on top end cell equals cell 2 open parentheses table row 3 row cell negative 2 end cell row 1 end table close parentheses minus 3 open parentheses table row 2 row 0 row cell negative 3 end cell end table close parentheses plus open parentheses table row 0 row 1 row cell negative 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 6 row cell negative 4 end cell row 2 end table close parentheses minus open parentheses table row 6 row 0 row cell negative 9 end cell end table close parentheses plus open parentheses table row 0 row 1 row cell negative 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 row cell negative 3 end cell row 9 end table close parentheses end cell end table

Vektor yang mewakili 2 a with rightwards arrow on top minus 3 b with rightwards arrow on top plus c with rightwards arrow on top equals negative 3 j plus 9 k 

Oleh karena itu, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

H. Eka

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 06 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

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.

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.

Roboguru

Jika diketahui vektor  serta  resultan dari  dan , maka hasil dari  adalah...

Pembahasan Soal:

Diketahui top enclose c resultan dari top enclose a dan top enclose b, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose c end cell equals cell top enclose a plus top enclose b end cell row blank equals cell open parentheses table row cell negative 8 end cell row cell negative 8 end cell end table close parentheses plus open parentheses table row 3 row cell negative 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 5 end cell row cell negative 10 end cell end table close parentheses end cell end table 

Menentukan hasil dari top enclose 2 b end enclose minus top enclose c

table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose 2 b end enclose minus top enclose c end cell equals cell 2 open parentheses table row 3 row cell negative 2 end cell end table close parentheses minus open parentheses table row cell negative 5 end cell row cell negative 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row 6 row cell negative 4 end cell end table close parentheses minus open parentheses table row cell negative 5 end cell row cell negative 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 6 minus left parenthesis negative 5 right parenthesis end cell row cell negative 4 minus left parenthesis negative 10 right parenthesis end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 6 plus 5 end cell row cell negative 4 plus 10 end cell end table close parentheses end cell row blank equals cell open parentheses table row 11 row 6 end table close parentheses end cell end table 

Jadi, jawaban yang benar adalah E.

 

Roboguru

Jika , dan , maka panjang vektor adalah ...

Pembahasan Soal:

Misalkan terdapat vektor straight a with rightwards arrow on top equals open parentheses table row cell straight a subscript 1 end cell row cell straight a subscript 2 end cell end table close parentheses equals straight a subscript 1 straight i with rightwards arrow on top plus straight a subscript 2 straight j with rightwards arrow on top, straight b with rightwards arrow on top equals open parentheses table row cell straight b subscript 1 end cell row cell straight b subscript 2 end cell end table close parentheses equals straight b subscript 1 straight i with rightwards arrow on top plus straight b subscript 2 straight j with rightwards arrow on top dan straight z adalah skalar. maka berlaku:

open parentheses straight i close parentheses space straight a with rightwards arrow on top plus-or-minus straight b with rightwards arrow on top equals open parentheses table row cell straight a subscript 1 plus-or-minus straight b subscript 1 end cell row cell straight a subscript 2 plus-or-minus straight b subscript 2 end cell end table close parentheses equals open parentheses straight a subscript 1 plus-or-minus straight b subscript 1 close parentheses straight i with rightwards arrow on top plus open parentheses straight a subscript 2 plus-or-minus straight b subscript 2 close parentheses straight j with rightwards arrow on top left parenthesis ii right parenthesis space straight z straight a with rightwards arrow on top equals open parentheses table row cell za subscript 1 end cell row cell za subscript 2 end cell end table close parentheses equals za subscript 1 straight i with rightwards arrow on top plus za subscript 2 straight j with rightwards arrow on top

Selain itu, untuk mencari panjang vektor straight a with rightwards arrow on top equals open parentheses table row cell straight a subscript 1 end cell row cell straight a subscript 2 end cell end table close parentheses equals straight a subscript 1 straight i with rightwards arrow on top plus straight a subscript 2 straight j with rightwards arrow on top adalah:

open vertical bar straight a with rightwards arrow on top close vertical bar equals square root of straight a subscript 1 squared plus straight a subscript 2 squared end root .

Berdasarkan uraian tentang vektor tersebut, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight d with rightwards arrow on top end cell equals cell 3 straight a with rightwards arrow on top minus 2 straight b with rightwards arrow on top plus straight c with rightwards arrow on top end cell row blank equals cell 3 open parentheses table row 1 row 3 end table close parentheses minus 2 open parentheses table row 0 row 1 end table close parentheses plus open parentheses table row 2 row 5 end table close parentheses end cell row blank equals cell open parentheses table row 3 row 9 end table close parentheses minus open parentheses table row 0 row 2 end table close parentheses plus open parentheses table row 2 row 5 end table close parentheses end cell row blank equals cell open parentheses table row cell 3 minus 0 plus 2 end cell row cell 9 minus 2 plus 5 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

Panjang vektor table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight d 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 5 row 12 end table close parentheses end cell end table adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight d 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 13 end table

Dengan demikian, panjang vektor straight d with rightwards arrow on top equals 3 straight a with rightwards arrow on top minus 2 straight b with rightwards arrow on top plus straight c with rightwards arrow on top yaitu 13.

Oleh karena itu, jawaban yang benar adalah C.

Roboguru

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

Pembahasan Soal:

Diketahui bahwa vektor a with rightwards arrow on top,b with rightwards arrow on top, dan c with rightwards arrow on top merupakan vektor basis (i,j,k) yang berada pada dimensi tiga yang dapat diubah ke vektor baris berada pada dimensi tiga sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell 3 i with rightwards arrow on top plus 1 half j with rightwards arrow on top minus 1 half k with rightwards arrow on top ⟶ a with rightwards arrow on top equals open parentheses 3 comma 1 half comma negative 1 half close parentheses end cell row blank blank blank row cell b with rightwards arrow on top end cell equals cell i with rightwards arrow on top plus 5 j with rightwards arrow on top minus k with rightwards arrow on top ⟶ b with rightwards arrow on top equals left parenthesis 1 , 5 comma negative 1 right parenthesis end cell row blank blank blank row cell c with rightwards arrow on top end cell equals cell 3 over 2 i with rightwards arrow on top ⟶ c with rightwards arrow on top equals open parentheses 3 over 2 comma 0 , 0 close parentheses end cell end table

maka

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

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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