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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

Pertanyaan

Diketahui straight A open parentheses negative 2 comma space 1 comma space 3 close parenthesesstraight B open parentheses negative 3 comma space 1 comma space 2 close parentheses, dan straight C open parentheses 3 comma space 2 comma space minus 1 close parentheses. Jika a with rightwards arrow on topb with rightwards arrow on top, dan c with rightwards arrow on top merupakan vektor posisi dari straight Astraight B, dan straight C, nyatakan vektor-vektor berikut ke dalam bentuk vektor satuan i with rightwards arrow on topj with rightwards arrow on top, dan k with rightwards arrow on top.space

c. 3 c with rightwards arrow on top plus 4 a with rightwards arrow on top minus 5 b with rightwards arrow on topspace 

S. Dwi

Master Teacher

Jawaban terverifikasi

Jawaban

 vektor 3 c with rightwards arrow on top plus 4 a with rightwards arrow on top minus 5 b with rightwards arrow on top dalam bentuk vektor satuan i with rightwards arrow on top, j with rightwards arrow on top, dan k with rightwards arrow on top adalah  table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 16 i with rightwards arrow on top plus 5 j with rightwards arrow on top minus k with rightwards arrow on top end cell end table.

Pembahasan

Jawaban yang benar untuk pertanyaan c adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 16 i with rightwards arrow on top plus 5 j with rightwards arrow on top minus k with rightwards arrow on top end cell end table.

c with rightwards arrow on top merupakan vektor posisi dari titik straight C open parentheses 3 comma space 2 comma space minus 1 close parentheses dan dapat dinyatakan sebagai berikut.spacespace

c with rightwards arrow on top equals 3 i with rightwards arrow on top plus 2 j with rightwards arrow on top minus k with rightwards arrow on topspace space 

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

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

Sehingga, dapat diperoleh:space

 table attributes columnalign right center left columnspacing 0px end attributes row cell 3 c with rightwards arrow on top end cell equals cell 3 open parentheses 3 i with rightwards arrow on top plus 2 j with rightwards arrow on top minus k with rightwards arrow on top close parentheses end cell row blank equals cell 9 i with rightwards arrow on top plus 6 j with rightwards arrow on top minus 3 k with rightwards arrow on top end cell row cell 4 a with rightwards arrow on top end cell equals cell 4 open parentheses negative 2 i with rightwards arrow on top plus j with rightwards arrow on top plus 3 k with rightwards arrow on top close parentheses end cell row blank equals cell negative 8 i with rightwards arrow on top plus 4 j with rightwards arrow on top plus 12 k with rightwards arrow on top end cell row cell 5 b with rightwards arrow on top end cell equals cell 5 open parentheses negative 3 i with rightwards arrow on top plus j with rightwards arrow on top plus 2 k with rightwards arrow on top close parentheses end cell row blank equals cell negative 15 i with rightwards arrow on top plus 5 j with rightwards arrow on top plus 10 k with rightwards arrow on top end cell end tablespace space 

Ingat!space

  • Untuk penjumlahan dua vektor atau lebih, dilakukan dengan menjumlahkan elemen-elemen yang sejenis, seperti berikut:space

p with rightwards arrow on top plus q with rightwards arrow on top plus r with rightwards arrow on top equals open parentheses x subscript 1 plus x subscript 2 plus x subscript 3 close parentheses i with rightwards arrow on top plus open parentheses y subscript 1 plus y subscript 2 plus y subscript 3 close parentheses j with rightwards arrow on top plus open parentheses z subscript 1 plus z subscript 2 plus z subscript 3 close parentheses k with rightwards arrow on topspace 

  • Untuk pengurangan dua vektor atau lebih, dilakukan dengan mengurangi elemen-elemen yang sejenis, seperti berikut:space

p with rightwards arrow on top minus q with rightwards arrow on top minus r with rightwards arrow on top equals open parentheses x subscript 1 minus x subscript 2 minus x subscript 3 close parentheses i with rightwards arrow on top plus open parentheses y subscript 1 minus y subscript 2 minus y subscript 3 close parentheses j with rightwards arrow on top plus open parentheses z subscript 1 minus z subscript 2 minus z subscript 3 close parentheses k with rightwards arrow on topspace 

spaceJadi, 3 c with rightwards arrow on top plus 4 a with rightwards arrow on top minus 5 b with rightwards arrow on top dapat diperoleh sebagai berikut.spacespace

begin mathsize 12px style 3 c with rightwards arrow on top plus 4 a with rightwards arrow on top minus 5 b with rightwards arrow on top equals open parentheses 9 i with rightwards arrow on top plus 6 j with rightwards arrow on top minus 3 k with rightwards arrow on top close parentheses plus open parentheses negative 8 i with rightwards arrow on top plus 4 j with rightwards arrow on top plus 12 k with rightwards arrow on top close parentheses minus open parentheses negative 15 i with rightwards arrow on top plus 5 j with rightwards arrow on top plus 10 k with rightwards arrow on top close parentheses equals 16 i with rightwards arrow on top plus 5 j with rightwards arrow on top minus k with rightwards arrow on top end stylespace  

Dengan demikian, vektor 3 c with rightwards arrow on top plus 4 a with rightwards arrow on top minus 5 b with rightwards arrow on top dalam bentuk vektor satuan i with rightwards arrow on top, j with rightwards arrow on top, dan k with rightwards arrow on top adalah  table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 16 i with rightwards arrow on top plus 5 j with rightwards arrow on top minus k with rightwards arrow on top end cell end table.

43

3.0 (1 rating)

Pertanyaan serupa

Diketahui titik A(5, 2, −3), B(6, 1, 4), C(−3, −2, −1), dan D(−1. −4. 13). Nyatakan ke dalam i, j​, dan k vektor-vektor yang diwakili oleh: c. BC−2DC,

111

4.5

Jawaban terverifikasi

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