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Pertanyaan

Diketahui titik straight A open parentheses 5 comma space 2 comma space minus 3 close parenthesesstraight B open parentheses 6 comma space 1 comma space 4 close parenthesesstraight C open parentheses negative 3 comma space minus 2 comma space minus 1 close parentheses, dan straight D open parentheses negative 1. space minus 4. space 13 close parentheses. Nyatakan ke dalam straight i with rightwards arrow on top comma space straight j with rightwards arrow on top comma space dan space straight k with rightwards arrow on top vektor-vektor yang diwakili oleh:space

c. BC with rightwards arrow on top minus 2 DC with rightwards arrow on top,space

U. Istinaro

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

 BC with rightwards arrow on top minus 2 DC with rightwards arrow on top equals negative 5 straight i with rightwards arrow on top minus 7 straight j with rightwards arrow on top plus 23 straight k with rightwards arrow on top.space 

Pembahasan

c. Jawaban yang benar untuk pertanyaan c adalah BC with rightwards arrow on top minus 2 DC with rightwards arrow on top equals negative 5 straight i with rightwards arrow on top minus 7 straight j with rightwards arrow on top plus 23 straight k with rightwards arrow on top.space

Hasil perkalian suatu vektor straight a with rightwards arrow on top equals straight x straight i with rightwards arrow on top plus straight y straight j with rightwards arrow on top plus straight z straight k with rightwards arrow on top dengan straight m suatu skalar yaitu:space

table attributes columnalign right center left columnspacing 0px end attributes row cell straight m straight a with rightwards arrow on top end cell equals cell straight m open parentheses straight x straight i with rightwards arrow on top plus straight y straight j with rightwards arrow on top plus straight z straight k with rightwards arrow on top close parentheses end cell row blank equals cell mx straight i with rightwards arrow on top plus my straight j with rightwards arrow on top plus mz straight k with rightwards arrow on top end cell end tablespace 

Sehingga,space

table attributes columnalign right center left columnspacing 0px end attributes row cell BC with rightwards arrow on top end cell equals cell straight c with rightwards arrow on top minus straight b with rightwards arrow on top end cell row blank equals cell open parentheses negative 3 straight i with rightwards arrow on top minus 2 straight j with rightwards arrow on top minus straight k with rightwards arrow on top close parentheses minus open parentheses 6 straight i with rightwards arrow on top plus straight j with rightwards arrow on top plus 4 straight k with rightwards arrow on top close parentheses end cell row blank equals cell negative 9 straight i with rightwards arrow on top minus 3 straight j with rightwards arrow on top minus 5 straight k with rightwards arrow on top end cell end tablespace 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 DC with rightwards arrow on top end cell equals cell 2 open parentheses straight c with rightwards arrow on top minus straight d with rightwards arrow on top close parentheses end cell row blank equals cell 2 open parentheses open parentheses negative 3 straight i with rightwards arrow on top minus 2 straight j with rightwards arrow on top minus straight k with rightwards arrow on top close parentheses minus open parentheses negative straight i with rightwards arrow on top minus 4 straight j with rightwards arrow on top plus 13 straight k with rightwards arrow on top close parentheses close parentheses end cell row blank equals cell 2 open parentheses negative 2 straight i with rightwards arrow on top plus 2 straight j with rightwards arrow on top minus 14 straight k with rightwards arrow on top close parentheses end cell row blank equals cell negative 4 straight i with rightwards arrow on top plus 4 straight j with rightwards arrow on top minus 28 straight k with rightwards arrow on top end cell end tablespace 

Jadi, BC with rightwards arrow on top minus 2 DC with rightwards arrow on top dapat ditentukan sebagai berikut:space

table attributes columnalign right center left columnspacing 0px end attributes row cell BC with rightwards arrow on top minus 2 DC with rightwards arrow on top end cell equals cell open parentheses negative 9 straight i with rightwards arrow on top minus 3 straight j with rightwards arrow on top minus 5 straight k with rightwards arrow on top close parentheses minus open parentheses negative 4 straight i with rightwards arrow on top plus 4 straight j with rightwards arrow on top minus 28 straight k with rightwards arrow on top close parentheses end cell row blank equals cell negative 5 straight i with rightwards arrow on top minus 7 straight j with rightwards arrow on top plus 23 straight k with rightwards arrow on top end cell end tablespace 

Dengan demikian, BC with rightwards arrow on top minus 2 DC with rightwards arrow on top equals negative 5 straight i with rightwards arrow on top minus 7 straight j with rightwards arrow on top plus 23 straight k with rightwards arrow on top.space 

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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-vektor berikut ke dalam bentuk vektor satuan i, j​, dan k. c. 3c+4a−5b

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