Roboguru

Diketahui  dan . Tentukan: a.

Pertanyaan

Diketahui a with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row 1 row 2 end table close parentheses dan b with rightwards arrow on top equals open parentheses table row 7 row 0 row cell negative 5 end cell end table close parentheses. Tentukan:
a. a with rightwards arrow on top plus b with rightwards arrow on top 

Pembahasan Soal:

Operasi penjumlahan vektor dapat dihitung seperti berikut,

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 table row cell negative 3 end cell row 1 row 2 end table close parentheses plus open parentheses table row 7 row 0 row cell negative 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 plus 7 end cell row cell 1 plus 0 end cell row cell 2 minus 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row 4 row 1 row cell negative 3 end cell end table close parentheses end cell end table 

Jadi, hasil dari penjumlahan vektor di atas adalah open parentheses table row 4 row 1 row cell negative 3 end cell end table close parentheses.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Kumaralalita

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 01 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika  dan  maka

Pembahasan Soal:

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose a end cell equals cell open square brackets 3 comma 2 comma negative 1 close square brackets end cell row cell top enclose b end cell equals cell open square brackets 5 comma negative 1 comma 6 close square brackets end cell end table

Perhatikan perhitungan berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose a plus top enclose b end cell equals cell open square brackets 3 comma 2 comma negative 1 close square brackets plus open square brackets 5 comma negative 1 comma 6 close square brackets end cell row blank equals cell open square brackets 3 plus 5 comma space 2 plus open parentheses negative 1 close parentheses comma space open parentheses negative 1 close parentheses plus 6 close square brackets end cell row blank equals cell open square brackets 8 comma space 1 comma space 5 close square brackets end cell end table

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 cell top enclose b 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 square brackets 8 comma space 1 comma space 5 close square brackets end cell end table.

Oleh karena itu, jawaban yang benar adalah B.

0

Roboguru

Diberikan vektor-vektor  dan vektor . Jika  dan  sejajar maka

Pembahasan Soal:

Jika vektor p with rightwards arrow on top sejajar vektor q with rightwards arrow on top, maka p with rightwards arrow on top equals k q with rightwards arrow on top dengan k skalar, k element of R

Pada soal di atas, apabila vektor a with rightwards arrow on top dan b with rightwards arrow on top sejajar, maka dapat ditentukan hubungan berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell k b with rightwards arrow on top end cell row cell open parentheses table row x row cell negative 3 end cell row 6 end table close parentheses end cell equals cell k open parentheses table row cell 1 minus y end cell row 3 row cell negative 1 minus x end cell end table close parentheses end cell end table

Diperoleh negative 3 equals 3 k space left right double arrow space k equals negative 1

Nilai x dan y adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row 6 equals cell k open parentheses negative 1 minus x close parentheses end cell row 6 equals cell negative 1 open parentheses negative 1 minus x close parentheses end cell row 6 equals cell 1 plus x end cell row x equals 5 end table

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell k open parentheses 1 minus y close parentheses end cell row 5 equals cell negative 1 open parentheses 1 minus y close parentheses end cell row 5 equals cell negative 1 plus y end cell row y equals 6 end table

Vektor a with rightwards arrow on top equals open parentheses table row x row cell negative 3 end cell row 6 end table close parentheses equals open parentheses table row 5 row cell negative 3 end cell row 6 end table close parentheses dan vektor b with rightwards arrow on top equals open parentheses table row cell 1 minus y end cell row 3 row cell negative open parentheses 1 plus x close parentheses end cell end table close parentheses equals open parentheses table row cell negative 5 end cell row 3 row cell negative 6 end cell end table close parentheses

Dapat ditentukan hasil operasi hitung pada vektor berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top plus 3 b with rightwards arrow on top end cell equals cell open parentheses table row 5 row cell negative 3 end cell row 6 end table close parentheses plus 3 open parentheses table row cell negative 5 end cell row 3 row cell negative 6 end cell end table close parentheses end cell row blank equals cell open parentheses table row 5 row cell negative 3 end cell row 6 end table close parentheses plus open parentheses table row cell negative 15 end cell row 9 row cell negative 18 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 10 end cell row 6 row cell negative 12 end cell 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 plus 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 b 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 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 6 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 minus 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 k with rightwards arrow on top end cell end table

Oleh karena itu, jawaban yang tepat adalah B.

0

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.

0

Roboguru

Diketahui vektor , vektor , dan vektor . Jika , dengan  bilangan real, maka nilai  adalah ...

Pembahasan Soal:

Nilai k pada operasi hitung vektor di atas adalah 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 k c with rightwards arrow on top end cell equals cell open parentheses table row 0 row cell negative 4 end cell end table close parentheses end cell row cell 2 open parentheses table row 3 row cell negative 2 end cell end table close parentheses minus 3 open parentheses table row 4 row 1 end table close parentheses plus k open parentheses table row cell negative 2 end cell row cell negative 1 end cell end table close parentheses end cell equals cell open parentheses table row 0 row cell negative 4 end cell end table close parentheses end cell row cell open parentheses table row 6 row cell negative 4 end cell end table close parentheses minus open parentheses table row 12 row 3 end table close parentheses plus open parentheses table row cell negative 2 k end cell row cell negative k end cell end table close parentheses end cell equals cell open parentheses table row 0 row cell negative 4 end cell end table close parentheses end cell row cell open parentheses table row cell negative 6 minus 2 k end cell row cell negative 7 minus k end cell end table close parentheses end cell equals cell open parentheses table row 0 row cell negative 4 end cell end table close parentheses end cell end table

Dari kesamaan vektor di atas diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 6 minus 2 k end cell equals 0 row cell negative 2 k end cell equals 6 row k equals cell negative 3 end cell end table

Oleh karena itu, jawaban yang tepat adalah B.

0

Roboguru

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

Pembahasan Soal:

Dengan menerapkan konsep penjumlahan dan pengurangan vektor serta perkalian vektor dengan skalar, diperoleh:

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 minus w with rightwards arrow on top end cell equals cell 2 open parentheses table row 3 row cell negative 1 end cell row 2 end table close parentheses plus open parentheses table row 1 row 4 row cell negative 3 end cell end table close parentheses minus open parentheses table row 5 row 2 row 1 end table close parentheses end cell row blank equals cell open parentheses table row 6 row cell negative 2 end cell row 4 end table close parentheses plus open parentheses table row 1 row 4 row cell negative 3 end cell end table close parentheses minus open parentheses table row 5 row 2 row 1 end table close parentheses end cell row blank equals cell open parentheses table row 2 row 0 row 0 end table close parentheses end cell row blank equals cell 2 i with hat on top end cell end table end style 

Jadi, hasil dari begin mathsize 14px style 2 u with rightwards arrow on top plus v with rightwards arrow on top minus w with rightwards arrow on top end style adalah begin mathsize 14px style 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 i with hat on top end cell end table end style.

Dengan demikian, jawaban yang tepat adalah A.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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