Roboguru

Diketahui vektor , , . Vektor  adalah ....

Pertanyaan

Diketahui vektor begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals open parentheses table row 3 row 2 row 1 end table close parentheses end stylebegin mathsize 14px style straight b with rightwards harpoon with barb upwards on top equals open parentheses table row cell negative 2 end cell row 3 row cell negative 1 end cell end table close parentheses end stylebegin mathsize 14px style straight c with rightwards harpoon with barb upwards on top equals open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses end style. Vektor begin mathsize 14px style 2 straight a with rightwards harpoon with barb upwards on top plus straight b with rightwards harpoon with barb upwards on top minus straight c with rightwards harpoon with barb upwards on top end style adalah ....

  1. begin mathsize 14px style open parentheses table row 3 row 3 row 4 end table close parentheses end style 

  2. begin mathsize 14px style open parentheses table row 3 row 4 row 3 end table close parentheses end style 

  3. begin mathsize 14px style open parentheses table row 3 row 4 row cell negative 1 end cell end table close parentheses end style 

  4. begin mathsize 14px style open parentheses table row 3 row cell negative 4 end cell row cell negative 1 end cell end table close parentheses end style 

  5. begin mathsize 14px style open parentheses table row cell negative 3 end cell row 3 row 4 end table close parentheses end style 

Pembahasan Soal:

Diketahui:

vektor begin mathsize 14px style straight a with rightwards harpoon with barb upwards on top equals open parentheses table row 3 row 2 row 1 end table close parentheses end stylebegin mathsize 14px style straight b with rightwards harpoon with barb upwards on top equals open parentheses table row cell negative 2 end cell row 3 row cell negative 1 end cell end table close parentheses end stylebegin mathsize 14px style straight c with rightwards harpoon with barb upwards on top equals open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses end style.

Ditanya:

Vektor begin mathsize 14px style 2 straight a with rightwards harpoon with barb upwards on top plus straight b with rightwards harpoon with barb upwards on top minus straight c with rightwards harpoon with barb upwards on top end style

Jawaban.

Dengan menerapkan konsep penjumlahan atau pengurangan vektor, maka diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight a with rightwards harpoon with barb upwards on top plus straight b with rightwards harpoon with barb upwards on top minus straight c with rightwards harpoon with barb upwards on top end cell equals cell 2 open parentheses table row 3 row 2 row 1 end table close parentheses plus open parentheses table row cell negative 2 end cell row 3 row cell negative 1 end cell end table close parentheses minus open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 2 times 3 end cell row cell 2 times 2 end cell row cell 2 times 1 end cell end table close parentheses plus open parentheses table row cell negative 2 end cell row 3 row cell negative 1 end cell end table close parentheses minus open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 6 row 4 row 2 end table close parentheses plus open parentheses table row cell negative 2 end cell row 3 row cell negative 1 end cell end table close parentheses minus open parentheses table row 1 row 3 row cell negative 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 6 minus 2 minus 1 end cell row cell 4 plus 3 minus 3 end cell row cell 2 minus 1 minus left parenthesis negative 2 right parenthesis end cell end table close parentheses end cell row blank equals cell open parentheses table row 3 row 4 row 3 end table close parentheses end cell end table end style 

Jadi, 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 straight a with rightwards harpoon with barb upwards 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 straight b with rightwards harpoon with barb upwards 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 straight c with rightwards harpoon with barb upwards 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 3 row 4 row 3 end table close parentheses end cell end table end style.

Oleh karena itu, Jawaban yang benar adalah B

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. RGFLLIMA

Terakhir diupdate 30 April 2021

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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

Diketahui , , dan   , Tentukan:

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 b with bar on top minus 3 c with bar on top plus 9 d with bar on top end cell equals cell 2 open parentheses table row cell negative 3 end cell row 3 end table close parentheses minus 3 open parentheses table row 2 row 9 end table close parentheses plus 9 open parentheses table row 4 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 6 end cell row 6 end table close parentheses minus open parentheses table row 6 row 27 end table close parentheses plus open parentheses table row 36 row cell negative 36 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 6 minus 6 plus 36 end cell row cell 6 minus 27 minus 36 end cell end table close parentheses end cell row blank equals cell open parentheses table row 24 row cell negative 57 end cell end table close parentheses end cell end table 

Jadi, hasil dari 2 b with bar on top minus 3 c with bar on top plus 9 d with bar on top adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 24 row cell negative 57 end cell end table close parentheses end cell end table

Roboguru

Diketahui , , dan .  dan  berturut-turut mewakili vektor  dan . Tentukan: d.

Pembahasan Soal:

Jika 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 dan b with rightwards arrow on top equals open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell end table close parentheses, maka a with rightwards arrow on top times b with rightwards arrow on top adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses times open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell end table close parentheses end cell row blank equals cell a subscript 1 b subscript 1 plus a subscript 2 b subscript 2 end cell end table 

Vektor Posisi adalah vektor yang berpangkal di pusat koordinat open parentheses 0 comma space 0 close parentheses dan berujung di suatu titik open parentheses x comma space y close parentheses.

Diketahui straight A open parentheses 2 comma space 6 comma space minus 5 close parentheses, straight B open parentheses negative 1 comma space 3 comma space 7 close parentheses, dan straight C open parentheses 4 comma space minus 1 comma space 8 close parentheses.

Nilai vektor posisi akan sama dengan koordinat titik ujungnya, maka tentukan AB with rightwards arrow on top dan BC with rightwards arrow on top.

table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell b with rightwards arrow on top minus a with rightwards arrow on top end cell row cell u with rightwards arrow on top end cell equals cell open parentheses table row cell negative 1 end cell row 3 row 7 end table close parentheses minus open parentheses table row 2 row 6 row cell negative 5 end cell end table close parentheses end cell row cell u with rightwards arrow on top end cell equals cell open parentheses table row cell negative 1 minus 2 end cell row cell 3 minus 6 end cell row cell 7 plus 5 end cell end table close parentheses end cell row cell u with rightwards arrow on top end cell equals cell open parentheses table row cell negative 3 end cell row cell negative 3 end cell row 12 end table close parentheses end cell row cell BC with rightwards arrow on top end cell equals cell c with rightwards arrow on top minus b with rightwards arrow on top end cell row cell v with rightwards arrow on top end cell equals cell open parentheses table row 4 row cell negative 1 end cell row 8 end table close parentheses minus open parentheses table row cell negative 1 end cell row 3 row 7 end table close parentheses end cell row cell v with rightwards arrow on top end cell equals cell open parentheses table row cell 4 plus 1 end cell row cell negative 1 minus 3 end cell row cell 8 minus 7 end cell end table close parentheses end cell row cell v with rightwards arrow on top end cell equals cell open parentheses table row 5 row cell negative 4 end cell row 1 end table close parentheses end cell end table   

d. open parentheses 2 u with rightwards arrow on top minus 3 v with rightwards arrow on top close parentheses squared

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 u with rightwards arrow on top minus 3 v with rightwards arrow on top close parentheses squared end cell row blank equals cell 4 open parentheses u with rightwards arrow on top close parentheses squared minus 12 open parentheses u with rightwards arrow on top times v with rightwards arrow on top close parentheses plus 9 open parentheses v with rightwards arrow on top close parentheses squared end cell row blank equals cell 4 open parentheses table row cell negative 3 end cell row cell negative 3 end cell row 12 end table close parentheses squared minus 12 open parentheses open parentheses table row cell negative 3 end cell row cell negative 3 end cell row cell negative 3 end cell end table close parentheses times open parentheses table row 5 row cell negative 4 end cell row 1 end table close parentheses close parentheses plus 9 open parentheses table row 5 row cell negative 4 end cell row 1 end table close parentheses squared end cell row blank equals cell 4 open parentheses open parentheses negative 3 close parentheses squared plus open parentheses negative 3 close parentheses squared plus 12 squared close parentheses minus 12 open parentheses negative 15 plus 12 plus 12 close parentheses plus 9 open parentheses 5 squared plus open parentheses negative 4 close parentheses squared plus 1 squared close parentheses end cell row blank equals cell 4 times 162 minus 12 times 9 plus 9 times 42 end cell row blank equals cell 648 minus 108 plus 378 end cell row blank equals 918 end table end style 

Jadi, Error converting from MathML to accessible text..

Roboguru

Diketahui vektor  dan , vektor . Tentukan: a) vektor  b) vektor

Pembahasan Soal:

Gunakan konsep operasi hitung vektor.

Diketahui vektor a with rightwards arrow on top equals 5 i with hat on top minus 12 j with hat on top dan b with rightwards arrow on top equals left parenthesis 3 comma space 4 right parenthesis equals 3 i with hat on top plus 4 j with hat on top, vektor c with rightwards arrow on top equals negative 2 i with hat on top minus 6 j with hat on top.

a) menentukan vektor a with rightwards arrow on top minus 2 b with rightwards arrow on top minus c with rightwards arrow on top

table attributes columnalign right center left columnspacing 2px end attributes row cell a with rightwards arrow on top minus 2 b with rightwards arrow on top minus c with rightwards arrow on top end cell equals cell open parentheses 5 i with hat on top minus 12 j with hat on top close parentheses minus 2 open parentheses 3 i with hat on top minus 4 j with hat on top close parentheses minus open parentheses negative 2 i with hat on top minus 6 j with hat on top close parentheses end cell row blank equals cell 5 i with hat on top minus 12 j with hat on top minus 6 i with hat on top plus 8 j with hat on top plus 2 i with hat on top plus 6 j with hat on top end cell row cell a with rightwards arrow on top minus 2 b with rightwards arrow on top minus c with rightwards arrow on top end cell equals cell i with hat on top plus 2 j with hat on top end cell end table

b) menentukan vektor 2 a with rightwards arrow on top plus b with rightwards arrow on top minus 1 half c with rightwards arrow on top

table attributes columnalign right center left columnspacing 2px end attributes row cell 2 a with rightwards arrow on top plus b with rightwards arrow on top minus 1 half c with rightwards arrow on top end cell equals cell 2 open parentheses 5 i with hat on top minus 12 j with hat on top close parentheses plus open parentheses 3 i with hat on top minus 4 j with hat on top close parentheses minus 1 half open parentheses negative 2 i with hat on top minus 6 j with hat on top close parentheses end cell row blank equals cell 10 i with hat on top minus 24 j with hat on top plus 3 i with hat on top minus 4 j with hat on top plus i with hat on top plus 3 j with hat on top end cell row cell 2 a with rightwards arrow on top plus b with rightwards arrow on top minus 1 half c with rightwards arrow on top end cell equals cell 14 i with hat on top minus 25 j with hat on top end cell end table

Jadi, diperoleh a with rightwards arrow on top minus 2 b with rightwards arrow on top minus c with rightwards arrow on top equals i with hat on top plus 2 j with hat on top dan 2 a with rightwards arrow on top plus b with rightwards arrow on top minus 1 half c with rightwards arrow on top equals 14 i with hat on top minus 25 j with hat on top.

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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