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Diketahui koordinat titik A(4,−3), B(−1,−5) dan C(−2,3). Jika a⇀, b⇀ dan c⇀ berturut-turut vektor posisi titik A, B, dan C, hasil 2a⇀−3b⇀+c⇀ adalah …

Pertanyaan

Diketahui koordinat titik begin mathsize 14px style straight A left parenthesis 4 comma space minus 3 right parenthesis end stylebegin mathsize 14px style straight B left parenthesis negative 1 comma space minus 5 right parenthesis end style dan begin mathsize 14px style straight C left parenthesis negative 2 comma space 3 right parenthesis end style. Jika a with rightwards harpoon with barb upwards on topb with rightwards harpoon with barb upwards on top dan begin mathsize 14px style c with rightwards harpoon with barb upwards on top end style berturut-turut vektor posisi titik straight A, straight B, dan straight C, hasil begin mathsize 14px style 2 a with rightwards harpoon with barb upwards on top minus 3 b with rightwards harpoon with barb upwards on top plus c with rightwards harpoon with barb upwards on top end style adalah begin mathsize 14px style horizontal ellipsis end style    

Pembahasan:

Vektor posisi titik straight A, straight B, dan straight C yaitu:

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

Dengan konsep perkalian vektor dengan skalar diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a with rightwards harpoon with barb upwards on top end cell equals cell 2 open parentheses 4 i with hat on top minus 3 j with hat on top close parentheses end cell row blank equals cell 8 i with hat on top minus 6 j with hat on top end cell row cell 3 b with rightwards harpoon with barb upwards on top end cell equals cell 3 open parentheses negative i with hat on top minus 5 j with hat on top close parentheses end cell row blank equals cell negative 3 i with hat on top minus 15 j with hat on top end cell end table end style

Operasi penjumlahan dan pengurangan vektor secara aljabar dari begin mathsize 14px style 2 a with rightwards harpoon with barb upwards on top minus 3 b with rightwards harpoon with barb upwards on top plus c with rightwards harpoon with barb upwards on top end style yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a with rightwards harpoon with barb upwards on top minus 3 b with rightwards harpoon with barb upwards on top plus c with rightwards harpoon with barb upwards on top end cell equals cell open parentheses 8 i with hat on top minus 6 j with hat on top close parentheses minus open parentheses negative 3 i with hat on top minus 15 j with hat on top close parentheses plus open parentheses negative 2 i with hat on top plus 3 j with hat on top close parentheses end cell row blank equals cell 8 i with hat on top minus 6 j with hat on top plus 3 i with hat on top plus 15 j with hat on top minus 2 i with hat on top plus 3 j with hat on top end cell row blank equals cell open parentheses 8 plus 3 minus 2 close parentheses i with hat on top plus open parentheses negative 6 plus 15 plus 3 close parentheses j with hat on top end cell row blank equals cell 9 i with hat on top plus 12 j with hat on top end cell end table

 

Jadi, hasil begin mathsize 14px style 2 a with rightwards harpoon with barb upwards on top minus 3 b with rightwards harpoon with barb upwards on top plus c with rightwards harpoon with barb upwards on top end style adalah begin mathsize 14px style 9 i with hat on top plus 12 j with hat on top end style.

Jawaban terverifikasi

Dijawab oleh:

G. Albiah

Mahasiswa/Alumni Universitas Galuh Ciamis

Terakhir diupdate 07 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Diketahui A(−2,1,3), B(−3,1,2), dan C(3,2,−1). Jika a, b, dan c merupakan vektor posisi dari A, B, dan C, nyatakan vektor berikut ke dalam bentuk vektor satuan i,j​,dank. c. 3c+4a−5b

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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