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Diketahui vektor ; ; dan . Hasil dari  adalah ...

Pertanyaan

Diketahui vektor begin mathsize 14px style a with rightwards arrow on top equals 4 i with rightwards arrow on top minus 3 over 2 j with rightwards arrow on top plus 2 k with rightwards arrow on top end style; begin mathsize 14px style b with rightwards arrow on top equals 2 i with rightwards arrow on top plus 5 j with rightwards arrow on top minus 3 k with rightwards arrow on top end style; dan begin mathsize 14px style c with rightwards arrow on top equals 2 j with rightwards arrow on top minus 3 k with rightwards arrow on top end style. Hasil dari begin mathsize 14px style a with rightwards arrow on top minus 1 half b with rightwards arrow on top plus 1 half c with rightwards arrow on top end style adalah ...

  1. begin mathsize 14px style 3 i with rightwards arrow on top plus 3 j with rightwards arrow on top plus 2 k with rightwards arrow on top end style 

  2. begin mathsize 14px style 3 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus 2 k with rightwards arrow on top end style 

  3. begin mathsize 14px style 5 i with rightwards arrow on top minus 5 j with rightwards arrow on top plus 2 k with rightwards arrow on top end style 

  4. begin mathsize 14px style 5 i with rightwards arrow on top minus 5 j with rightwards arrow on top plus 3 k with rightwards arrow on top end style 

  5. begin mathsize 14px style 5 i with rightwards arrow on top minus 5 j with rightwards arrow on top plus 5 k with rightwards arrow on top end style 

Pembahasan Soal:

Ubahlah vektor basis begin mathsize 14px style open parentheses i with rightwards arrow on top comma space j with rightwards arrow on top comma space k with rightwards arrow on top close parentheses end style menjadi vektor kolom agar perhitungan dapat dilakukan dengan mudah.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top minus 1 half b with rightwards arrow on top plus 1 half c with rightwards arrow on top end cell equals cell open parentheses table row 4 row cell negative 3 over 2 end cell row 2 end table close parentheses minus 1 half open parentheses table row 2 row 5 row cell negative 3 end cell end table close parentheses plus 1 half open parentheses table row 0 row 2 row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 4 row cell negative 3 over 2 end cell row 2 end table close parentheses minus open parentheses table row 1 row cell 5 over 2 end cell row cell negative 3 over 2 end cell end table close parentheses plus open parentheses table row 0 row 1 row cell negative 3 over 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 4 minus 1 plus 0 end cell row cell negative 3 over 2 minus 5 over 2 plus 1 end cell row cell 2 plus 3 over 2 minus 3 over 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 3 row cell negative 6 over 2 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses table row 3 row cell negative 3 end cell row 2 end table close parentheses end cell end table end style 

Sehingga, begin mathsize 14px style 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 1 half end cell 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 1 half end cell 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 3 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 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 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 2 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 end style.

Jadi, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Mahasiswa/Alumni Universitas Indraprasta PGRI

Terakhir diupdate 29 Maret 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui vektor , , . Jika vektor  mewakili , vektor  mewakili , dan vektor  mewakili , hitunglah !

Pembahasan Soal:

Dengan menerapkan konsep operasi vektor, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 b with rightwards arrow on top minus 3 c with rightwards arrow on top plus a with rightwards arrow on top end cell row blank equals cell 2 QR with rightwards arrow on top minus 3 PR with rightwards arrow on top plus PQ with rightwards arrow on top end cell row blank equals cell 2 open parentheses OR with rightwards arrow on top minus OQ with rightwards arrow on top close parentheses minus 3 open parentheses OR with rightwards arrow on top minus OP with rightwards arrow on top close parentheses plus open parentheses OQ with rightwards arrow on top minus OP with rightwards arrow on top close parentheses end cell row blank equals cell 2 OR with rightwards arrow on top minus 2 OQ with rightwards arrow on top minus 3 OR with rightwards arrow on top plus 3 OP with rightwards arrow on top plus OQ with rightwards arrow on top minus OP with rightwards arrow on top end cell row blank equals cell negative OR with rightwards arrow on top minus OQ with rightwards arrow on top plus 2 OP with rightwards arrow on top end cell row blank equals cell negative 1 open parentheses table row 7 row 4 end table close parentheses minus 1 open parentheses table row cell negative 1 end cell row 5 end table close parentheses plus 2 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 7 end cell row cell negative 4 end cell end table close parentheses minus open parentheses table row cell negative 1 end cell row 5 end table close parentheses plus open parentheses table row 6 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 row cell negative 13 end cell end table close parentheses end cell end table end style 

Jadi, vektor begin mathsize 14px style 2 b with rightwards arrow on top minus 3 c with rightwards arrow on top plus a with rightwards arrow on top end style adalah begin mathsize 14px style open parentheses table row 0 row cell negative 13 end cell end table close parentheses end style.

0

Roboguru

Jika , hasil operasi adalah ....

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 5 straight a with rightwards arrow on top minus 3 straight b with rightwards arrow on top end cell equals cell 5 left parenthesis 2 straight i with rightwards arrow on top plus straight j with hat on top minus 4 straight k with hat on top right parenthesis minus 3 left parenthesis 3 straight i with rightwards arrow on top minus 2 straight j with hat on top minus 5 straight k with hat on top right parenthesis end cell row blank equals cell straight i with rightwards arrow on top plus 11 straight j with hat on top minus 5 straight k with hat on top end cell end table end style

Jadi, jawaban yang tepat adalah B.

0

Roboguru

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.

1

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.

1

Roboguru

Jika , dan , maka vektor satuan adalah ...

Pembahasan Soal:

Vektor satuan dari vektor tiga dimensi 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 row cell straight a subscript 3 end cell end table close parentheses adalah sebagai berikut.

fraction numerator straight a with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top close vertical bar end fraction equals fraction numerator open parentheses straight a subscript 1 comma space straight a subscript 2 comma space straight a subscript 3 close parentheses over denominator square root of straight a subscript 1 squared plus straight a subscript 2 squared plus straight a subscript 3 squared end root end fraction.

Sebelum mencari vektor satuan dari straight d with rightwards arrow on top, hitunglah operasi vektornya terlebih dahulu, yaitu:

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

Selanjutnya, vektor satuan straight d with rightwards arrow on top adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight d with rightwards arrow on top over denominator open vertical bar straight d with rightwards arrow on top close vertical bar end fraction end cell equals cell fraction numerator open parentheses negative 2 comma space 6 comma space 3 close parentheses over denominator square root of open parentheses negative 2 close parentheses squared plus 6 squared plus 3 squared end root end fraction end cell row blank equals cell fraction numerator open parentheses negative 2 comma space 6 comma space 3 close parentheses over denominator square root of 4 plus 36 plus 9 end root end fraction end cell row blank equals cell fraction numerator open parentheses negative 2 comma space 6 comma space 3 close parentheses over denominator square root of 49 end fraction end cell row blank equals cell fraction numerator open parentheses negative 2 comma space 6 comma space 3 close parentheses over denominator 7 end fraction end cell row blank equals cell open parentheses negative 2 over 7 comma space 6 over 7 comma space 3 over 7 close parentheses end cell row blank equals cell negative 2 over 7 straight i with rightwards arrow on top plus 6 over 7 straight j with rightwards arrow on top plus 3 over 7 straight k with rightwards arrow on top end cell end table

Dengan demikian, jawaban yang benar 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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