Roboguru

Diketahui titik . Tentukan dan nyatakan vektor-vekot berikut dalam bentuk kombinasi linear.

Pertanyaan

Diketahui titik straight A open parentheses 3 comma 7 close parentheses space dan space straight B open parentheses negative 5 comma 2 close parentheses. Tentukan dan nyatakan vektor-vekot berikut dalam bentuk kombinasi linear.

straight a. space AB with rightwards arrow on top straight b. space BA with rightwards arrow on top

Pembahasan Soal:

Penyajian dalam bentuk vektor kombinasi linear adalah :

straight a. space AB with rightwards arrow on top equals straight B minus straight A equals open parentheses negative 5 minus 3 close parentheses top enclose straight i plus open parentheses 2 minus 7 close parentheses top enclose straight j equals negative 8 top enclose straight i minus 5 top enclose straight j straight b. space BA with rightwards arrow on top equals straight A minus straight B equals open parentheses 3 minus left parenthesis negative 5 right parenthesis close parentheses top enclose straight i plus open parentheses 7 minus 2 close parentheses top enclose straight j equals 8 top enclose straight i plus 5 top enclose straight j

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

H. Janatu

Mahasiswa/Alumni Universitas Riau

Terakhir diupdate 02 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui vektor-vektor . Nyatakan setiap vektor berikut ke dalam vektor satuan  dan tentukan besarnya. c.

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a with rightwards arrow on top minus b with rightwards arrow on top plus 3 c with rightwards arrow on top end cell equals cell 2 left parenthesis 2 i with rightwards arrow on top minus 3 j with rightwards arrow on top right parenthesis minus left parenthesis negative 4 i with rightwards arrow on top minus j with rightwards arrow on top right parenthesis plus 3 left parenthesis negative i with rightwards arrow on top plus 2 j with rightwards arrow on top right parenthesis end cell row blank equals cell left parenthesis 4 i with rightwards arrow on top minus 6 j with rightwards arrow on top right parenthesis minus left parenthesis negative 4 i with rightwards arrow on top minus j with rightwards arrow on top right parenthesis plus left parenthesis negative 3 i with rightwards arrow on top plus 6 j with rightwards arrow on top right parenthesis end cell row blank equals cell 5 i with rightwards arrow on top plus j with rightwards arrow on top end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar 2 a with rightwards arrow on top minus b with rightwards arrow on top plus 3 c with rightwards arrow on top close vertical bar end cell equals cell square root of 5 squared plus 1 squared end root end cell row blank equals cell square root of 25 plus 1 end root end cell row blank equals cell square root of 26 end cell end table end style 

jadi vektor 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 minus 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 3 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 5 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 cell j with rightwards arrow on top end cell end table

dan besar vektor 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 minus 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 3 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 blank space end table adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open vertical bar 2 a with rightwards arrow on top minus b with rightwards arrow on top plus 3 c with rightwards arrow on top close vertical bar 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 square root of 26 end cell end table

0

Roboguru

Jika diketaui suatu vektor dalam bidang datar yaitu dan . Tentukanlah

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 u with rightwards harpoon with barb upwards on top minus 2 v with rightwards harpoon with barb upwards on top end cell equals cell 3 open parentheses negative j close parentheses minus 2 left parenthesis negative 3 j plus 4 i right parenthesis end cell row blank equals cell negative 3 j plus 6 j minus 8 i end cell row blank equals cell 3 j minus 8 i end cell row cell open vertical bar 3 u with rightwards harpoon with barb upwards on top minus 2 v with rightwards harpoon with barb upwards on top close vertical bar end cell equals cell square root of 3 squared plus left parenthesis negative 8 right parenthesis squared end root end cell row blank equals cell square root of 9 plus 64 end root end cell row blank equals cell square root of 73 end cell row blank blank blank row blank blank blank end table

Oleh karena itu, jawaban yang benar adalah C.

0

Roboguru

Diketahui vektor , , dan . Tentukan b.

Pembahasan Soal:

Ingat rumus penjumlahan dua vektor adalah sebagai berikut.

undefined 

Dari soal di atas, diketahui undefined dan begin mathsize 14px style c with rightwards arrow on top end style sebagai berikut.

begin mathsize 14px style a with rightwards arrow on top equals 2 i with hat on top plus 3 j with hat on top equals open parentheses table row 2 row 3 end table close parentheses c with rightwards arrow on top equals 4 j with hat on top equals open parentheses table row 0 row 4 end table close parentheses end style 

Dengan menggunakan rumus penjumlahan dua vektor di atas, maka diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top plus c with rightwards arrow on top end cell equals cell open parentheses table row 2 row 3 end table close parentheses plus open parentheses table row 0 row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 2 plus 0 end cell row cell 3 plus 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row 7 end table close parentheses end cell row blank equals cell 2 i with hat on top plus 7 j with hat on top end cell end table end style 

Dengan demikian nilai dari begin mathsize 14px style a with rightwards arrow on top plus c with rightwards arrow on top end style adalah begin mathsize 14px style 2 i with hat on top plus 7 j with hat on top end style.

0

Roboguru

Jika  maka

Pembahasan Soal:

Jika v with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 3 end table close parentheses.

Ingat!

  • Suatu vektor a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses dapat dinyatakan sebagai kombinasi linear dari vektor basis i with rightwards arrow on top dan j with rightwards arrow on top tersebut, yaitu a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses equals a subscript 1 i with rightwards arrow on top plus a subscript 2 j with rightwards arrow on top.

Sehingga:

v with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 3 end table close parentheses equals negative 2 i with rightwards arrow on top plus 3 j with rightwards arrow on top 

Jadi, jawaban yang tepat adalah A.

0

Roboguru

Diketahui: Tentukan  !

Pembahasan Soal:

Diketahui :

straight a with rightwards arrow on top equals straight i with rightwards arrow on top plus straight j with rightwards arrow on top comma space straight b equals 2 straight i with rightwards arrow on top minus 3 straight j with rightwards arrow on top plus stack straight k space with rightwards arrow on top dan stack space straight c with rightwards arrow on top equals 4 straight j with rightwards arrow on top plus 3 straight k with rightwards arrow on top

Sehingga, dengan menggunakan konsep cross product pada vektor:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top cross times straight b with rightwards arrow on top end cell equals cell open vertical bar table row straight i straight j straight k row 1 1 0 row 2 cell negative 3 end cell 1 end table close vertical bar end cell row blank equals cell open vertical bar table row 1 0 row cell negative 3 end cell 1 end table close vertical bar straight i plus open vertical bar table row 0 1 row 1 2 end table close vertical bar straight j plus open vertical bar table row 1 1 row 2 cell negative 3 end cell end table close vertical bar straight k end cell row cell straight a with rightwards arrow on top cross times straight b with rightwards arrow on top end cell equals cell 4 straight i minus straight j minus 5 straight k end cell end table

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight a with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cross times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight 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 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight i 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 straight j 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 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight k end table

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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