Roboguru

Pada segitiga  diketahui  dan  Titik  pada  sehingga  Komponen vektor  adalah

Pertanyaan

Pada segitiga begin mathsize 14px style text ABC, end text end style diketahui begin mathsize 14px style text A end text open parentheses negative 2 comma 2 comma negative 5 close parentheses comma space text B end text open parentheses 3 comma negative 8 comma 5 close parentheses end style dan begin mathsize 14px style text C end text open parentheses negative 1 comma negative 3 comma 0 close parentheses. end style Titik begin mathsize 14px style text Q end text end style pada begin mathsize 14px style stack A B with bar on top end style sehingga begin mathsize 14px style stack A Q with bar on top colon stack Q B with bar on top equals 3 colon 2. end style Komponen vektor begin mathsize 14px style stack C Q with rightwards harpoon with barb upwards on top end style adalah begin mathsize 14px style horizontal ellipsis end style 

Pembahasan Soal:

Diketahui :

text A end text open parentheses negative 2 comma 2 comma negative 5 close parentheses
text B end text open parentheses 3 comma negative 8 comma 5 close parentheses
text C end text open parentheses negative 1 comma negative 3 comma 0 close parentheses
 stack A Q with bar on top colon stack Q B with bar on top equals 3 colon 2

Ditanya :

    - Komponen vektor begin mathsize 14px style stack C Q with rightwards harpoon with barb upwards on top end style

Penyelesaian :

Tentukan terlebih dahulu Q dengan menggunakan rumus perbandingan vektor.

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A Q with bar on top colon stack Q B with bar on top end cell equals cell 3 colon 2 end cell row cell 2 A Q end cell equals cell 3 Q B end cell row cell 2 open parentheses Q minus A close parentheses end cell equals cell 3 open parentheses B minus Q close parentheses end cell row cell 2 Q minus 2 A end cell equals cell 3 B minus 3 Q end cell row cell 2 Q plus 3 Q end cell equals cell 3 B plus 2 A end cell row cell 5 Q end cell equals cell 3 B plus 2 A end cell row Q equals cell fraction numerator 3 B plus 2 A over denominator 5 end fraction end cell row blank equals cell fraction numerator open parentheses 3 open parentheses 3 comma negative 8 comma 5 close parentheses plus 2 open parentheses negative 2 comma 2 comma negative 5 close parentheses close parentheses over denominator 5 end fraction end cell row blank equals cell fraction numerator open parentheses 9 comma negative 24 comma 15 close parentheses plus open parentheses negative 4 comma 4 comma negative 10 close parentheses over denominator 5 end fraction end cell row blank equals cell fraction numerator open parentheses 5 comma negative 20 comma 5 close parentheses over denominator 5 end fraction end cell row Q equals cell open parentheses 1 comma negative 4 comma 1 close parentheses end cell end table

Selanjutnya akan dicari komponen vektor begin mathsize 14px style stack C Q with rightwards harpoon with barb upwards on top end style dengan substitusi nilai dari Q yang telah diperoleh.

table attributes columnalign right center left columnspacing 0px end attributes row cell C Q end cell equals cell Q minus C end cell row blank equals cell open parentheses 1 comma negative 4 comma 1 close parentheses minus open parentheses negative 1 comma negative 3 comma 0 close parentheses end cell row cell C Q end cell equals cell open parentheses 2 comma negative 1 comma 1 close parentheses end cell end table

Dengan demikian, komponen vektor stack C Q with rightwards harpoon with barb upwards on top adalah left parenthesis 2 comma negative 1 comma 1 right parenthesis.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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