Roboguru

Perhatikan gambar segi enam beraturan berikut.   Jika  dan  , nyatakan vektor  dalam  dan .

Pertanyaan

Perhatikan gambar segi enam beraturan berikut.
 

Jika begin mathsize 14px style stack A B with rightwards arrow on top equals u with rightwards arrow on top end style dan begin mathsize 14px style stack A F with rightwards arrow on top equals v with rightwards arrow on top end style , nyatakan vektor begin mathsize 14px style stack D F with rightwards arrow on top end style dalam begin mathsize 14px style u with rightwards arrow on top end style dan begin mathsize 14px style v with rightwards arrow on top end style.

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack A O with rightwards arrow on top end cell equals cell 2 left parenthesis stack A F with rightwards arrow on top plus stack A B with rightwards arrow on top right parenthesis end cell row blank equals cell 2 left parenthesis v with rightwards arrow on top plus u with rightwards arrow on top right parenthesis end cell row blank equals cell 2 v with rightwards arrow on top plus 2 u with rightwards arrow on top end cell row blank blank blank row cell stack E F with rightwards arrow on top end cell equals cell negative stack A O with rightwards arrow on top end cell row blank equals cell negative 2 v with rightwards arrow on top minus 2 u with rightwards arrow on top end cell row blank blank blank row cell stack D E with rightwards arrow on top end cell equals cell negative stack A B with rightwards arrow on top end cell row blank equals cell negative u with rightwards arrow on top end cell row blank blank blank row cell stack D F with rightwards arrow on top end cell equals cell stack D E with rightwards arrow on top plus stack E F with rightwards arrow on top end cell row blank equals cell negative u with rightwards arrow on top minus 2 u with rightwards arrow on top minus 2 v with rightwards arrow on top end cell row blank equals cell negative 3 u with rightwards arrow on top minus 2 v with rightwards arrow on top end cell end table end style

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 30 Maret 2021

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Pertanyaan yang serupa

Diketahui vektor , , dan . Jika vektor  mewakili , vektor  mewakili , dan vektor  mewakili , tentukan

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell stack P Q with rightwards arrow on top end cell row blank equals cell stack P O with rightwards arrow on top plus stack O Q with rightwards arrow on top end cell row blank equals cell negative open parentheses table row 3 row cell negative 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row 5 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell row 7 end table close parentheses end cell row blank blank blank end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell b with rightwards arrow on top end cell equals cell stack Q O with rightwards arrow on top plus stack O R with rightwards arrow on top end cell row blank equals cell negative open parentheses table row cell negative 1 end cell row 5 end table close parentheses plus open parentheses table row 7 row 4 end table close parentheses end cell row blank equals cell open parentheses table row 8 row cell negative 1 end cell end table close parentheses end cell row blank blank blank end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c with rightwards arrow on top end cell equals cell stack P O with rightwards arrow on top plus stack O R with rightwards arrow on top end cell row blank equals cell negative open parentheses table row 3 row cell negative 2 end cell end table close parentheses plus open parentheses table row 7 row 4 end table close parentheses end cell row blank equals cell open parentheses table row 4 row 6 end table close parentheses end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 a with rightwards arrow on top minus 6 b with rightwards arrow on top plus c with rightwards arrow on top end cell equals cell 4 open parentheses table row cell negative 4 end cell row 7 end table close parentheses minus 6 open parentheses table row 8 row cell negative 1 end cell end table close parentheses plus open parentheses table row 4 row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 16 end cell row 28 end table close parentheses minus open parentheses table row 48 row cell negative 6 end cell end table close parentheses plus open parentheses table row 4 row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 60 end cell row 28 end table close parentheses end cell end table end style      

Roboguru

Gambarkan penjumlahan dan pengurangan dengan cara segitiga atau jajar genjang : a.

Pembahasan Soal:

Roboguru

Tentukanlah hasil penjumlahan dan pengurangan vektor-vektor berikut secara geometri menggunakan metode segitiga/ jajargenjang/ poligon dan secara aljabar. 10.

Pembahasan Soal:

Metode Segitiga

 

Metode Jajargenjang

 

Secara Aljabar

begin mathsize 14px style v with rightwards arrow on top equals open parentheses table row cell x subscript 2 minus x subscript 1 end cell row cell y subscript 2 minus y subscript 1 end cell end table close parentheses equals open parentheses table row cell v subscript 1 end cell row cell v subscript 2 end cell end table close parentheses a with rightwards arrow on top equals open parentheses table row cell 6 minus 2 end cell row cell negative 1 minus 0 end cell end table close parentheses equals open parentheses table row 4 row cell negative 1 end cell end table close parentheses b with rightwards arrow on top equals open parentheses table row cell 3 minus 1 end cell row cell 4 minus 1 end cell end table close parentheses equals open parentheses table row 2 row 3 end table close parentheses c with rightwards arrow on top equals open parentheses table row cell 3 minus 5 end cell row cell 2 minus 1 end cell end table close parentheses equals open parentheses table row cell negative 2 end cell row 1 end table close parentheses d with rightwards arrow on top equals open parentheses table row cell 6 minus 7 end cell row cell 1 minus 3 end cell end table close parentheses equals open parentheses table row cell negative 1 end cell row cell negative 2 end cell end table close parentheses  1 half a with rightwards arrow on top minus d with rightwards arrow on top equals 1 half open parentheses table row 4 row cell negative 1 end cell end table close parentheses minus open parentheses table row cell negative 1 end cell row cell negative 2 end cell end table close parentheses space space space space space space space space space space space space equals open parentheses table row cell 2 plus 1 end cell row cell negative 1 half plus 2 end cell end table close parentheses space space space space space space space space space space space space equals open parentheses table row 3 row cell 3 over 2 end cell end table close parentheses end style

Roboguru

Dari vektor-vektor berikut, lukis resultan dari persoalan berikut. b.

Pembahasan Soal:

        

Roboguru

Diketahui vektor , , dan . Jika vektor  mewakili , vektor  mewakili , dan vektor  mewakili , tentukan

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell stack P Q with rightwards arrow on top end cell row blank equals cell stack P O with rightwards arrow on top plus stack O Q with rightwards arrow on top end cell row blank equals cell negative open parentheses table row 3 row cell negative 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row 5 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell row 7 end table close parentheses end cell row blank blank blank end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell b with rightwards arrow on top end cell equals cell stack Q O with rightwards arrow on top plus stack O R with rightwards arrow on top end cell row blank equals cell negative open parentheses table row cell negative 1 end cell row 5 end table close parentheses plus open parentheses table row 7 row 4 end table close parentheses end cell row blank equals cell open parentheses table row 8 row cell negative 1 end cell end table close parentheses end cell row blank blank blank end table end style 

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 end cell equals cell 2 open parentheses table row cell negative 4 end cell row 7 end table close parentheses minus open parentheses table row 8 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 8 end cell row 14 end table close parentheses minus open parentheses table row 8 row cell negative 1 end cell end table close parentheses end cell row blank blank cell open parentheses table row cell negative 16 end cell row 15 end table close parentheses end cell end table end style  

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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