Roboguru

Perhatikan gambar di bawah ini.  dan , Jika ,  dan  masing-masing adalah vektor posisi dari titik A, B dan C make

Pertanyaan

Perhatikan gambar di bawah ini. BD space colon space DC equals 1 space colon space 2 dan AE space colon space EC equals 3 space colon space 1,

Jika a with bar on top, b with bar on top dan c with bar on top masing-masing adalah vektor posisi dari titik A, B dan C make stack E D with rightwards arrow on top equals... 

  1. 1 over 12 left parenthesis negative 3 a with rightwards arrow on top plus 8 b with rightwards arrow on top plus 5 c with rightwards arrow on top right parenthesis  

  2. 1 over 12 left parenthesis negative 3 a with rightwards arrow on top plus 8 b with rightwards arrow on top minus 5 c with rightwards arrow on top right parenthesis 

  3. negative 3 a with rightwards arrow on top plus 8 b with rightwards arrow on top minus 5 c with rightwards arrow on top 

  4. 1 third left parenthesis negative 3 a with rightwards arrow on top plus 5 b with rightwards arrow on top minus 8 c with rightwards arrow on top right parenthesis 

  5. 1 fourth left parenthesis negative 3 a with rightwards arrow on top minus 5 b with rightwards arrow on top plus 8 c with rightwards arrow on top right parenthesis 

Pembahasan Soal:

Diketahui BD space colon space DC equals 1 space colon space 2 dan AE space colon space EC equals 3 space colon space 1.

Ingat!

Pada vektor, stack A B with rightwards arrow on top didefinisikan dengan stack A B with rightwards arrow on top equals stack O B with rightwards arrow on top minus stack O A with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top.

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell BD space colon space DC end cell equals cell 1 space colon space 2 end cell row cell fraction numerator stack B D with rightwards arrow on top over denominator stack D C with rightwards arrow on top end fraction end cell equals cell 1 half end cell row cell 2 stack B D with rightwards arrow on top end cell equals cell stack D C with rightwards arrow on top end cell row cell 2 open parentheses d with rightwards arrow on top minus b with rightwards arrow on top close parentheses end cell equals cell c with rightwards arrow on top minus d with rightwards arrow on top end cell row cell 2 d with rightwards arrow on top minus 2 b with rightwards arrow on top end cell equals cell c with rightwards arrow on top minus d with rightwards arrow on top end cell row cell 2 d with rightwards arrow on top plus d with rightwards arrow on top minus c with rightwards arrow on top end cell equals cell 2 b with rightwards arrow on top end cell row cell 3 d with rightwards arrow on top minus c with rightwards arrow on top end cell equals cell 2 b with rightwards arrow on top space.... space left parenthesis 1 right parenthesis end cell row blank blank blank row cell AE space colon space EC end cell equals cell 3 space colon space 1 end cell row cell fraction numerator stack A E with rightwards arrow on top over denominator stack E C with rightwards arrow on top end fraction end cell equals cell 3 over 1 end cell row cell stack A E with rightwards arrow on top end cell equals cell 3 stack E C with rightwards arrow on top end cell row cell e with rightwards arrow on top minus a with rightwards arrow on top end cell equals cell 3 left parenthesis c with rightwards arrow on top minus e with rightwards arrow on top right parenthesis end cell row cell e with rightwards arrow on top minus a with rightwards arrow on top end cell equals cell 3 c with rightwards arrow on top minus 3 e with rightwards arrow on top end cell row cell e with rightwards arrow on top plus 3 e with rightwards arrow on top end cell equals cell a with rightwards arrow on top plus 3 c with rightwards arrow on top end cell row cell 4 e with rightwards arrow on top end cell equals cell a with rightwards arrow on top plus 3 c with rightwards arrow on top end cell row cell 4 e with rightwards arrow on top minus 3 c with rightwards arrow on top end cell equals cell a with rightwards arrow on top space.... space left parenthesis 2 right parenthesis end cell end table   

Kurangkan (1) dengan (2) dengan terlebih dahulu menyamakan koefisien pada d with rightwards arrow on top dan e with rightwards arrow on top, maka:

table row cell 3 d with rightwards arrow on top minus c with rightwards arrow on top equals 2 b with rightwards arrow on top end cell cell open vertical bar cross times 4 close vertical bar end cell cell 12 d with rightwards arrow on top minus 4 c with rightwards arrow on top equals 8 b with rightwards arrow on top end cell row cell 4 e with rightwards arrow on top minus 3 c with rightwards arrow on top equals a with rightwards arrow on top end cell cell open vertical bar cross times 3 close vertical bar end cell cell 12 e with rightwards arrow on top minus 9 c with rightwards arrow on top equals 3 a with rightwards arrow on top end cell end table     

Sehingga:

begin mathsize 12px style table row cell 12 d with rightwards arrow on top minus 4 c with rightwards arrow on top equals 8 b with rightwards arrow on top end cell row cell 12 e with rightwards arrow on top minus 9 c with rightwards arrow on top equals 3 a with rightwards arrow on top space space space space space space space space space space space space space space space space space space space space space minus end cell row cell 12 d with rightwards arrow on top minus 12 e with rightwards arrow on top plus 5 c with rightwards arrow on top equals 8 b with rightwards arrow on top minus 3 a with rightwards arrow on top end cell row cell 12 d with rightwards arrow on top minus 12 e with rightwards arrow on top equals 8 b with rightwards arrow on top minus 3 a with rightwards arrow on top minus 5 c with rightwards arrow on top end cell row cell 12 left parenthesis d with rightwards arrow on top minus e with rightwards arrow on top right parenthesis equals 8 b with rightwards arrow on top minus 3 a with rightwards arrow on top minus 5 c with rightwards arrow on top end cell row cell d with rightwards arrow on top minus e with rightwards arrow on top equals 1 over 12 open parentheses 8 b with rightwards arrow on top minus 3 a with rightwards arrow on top minus 5 c with rightwards arrow on top close parentheses end cell row cell stack E D with rightwards arrow on top equals 1 over 12 open parentheses 8 b with rightwards arrow on top minus 3 a with rightwards arrow on top minus 5 c with rightwards arrow on top close parentheses end cell row cell stack E D with rightwards arrow on top equals 1 over 12 left parenthesis negative 3 a with rightwards arrow on top plus 8 b with rightwards arrow on top minus 5 c with rightwards arrow on top right parenthesis end cell end table end style 

Jadi, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Juli 2021

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