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Vektor PQ ​ = 4 i + 2 k dan vektor PR = 2 i + j ​ + k . Jika PS = − 2 1 ​ PQ ​ maka vektor RS = ...

Vektor dan vektor . Jika maka vektor

  1. 4 straight i with rightwards arrow on top minus straight j with rightwards arrow on top minus 3 straight k with rightwards arrow on top

  2. 4 straight i with rightwards arrow on top plus straight j with rightwards arrow on top minus 3 straight k with rightwards arrow on top

  3. negative 4 straight i with rightwards arrow on top minus straight j with rightwards arrow on top minus 3 straight k with rightwards arrow on top

  4. negative 4 straight i with rightwards arrow on top minus straight j with rightwards arrow on top plus 3 straight k with rightwards arrow on top

  5. 4 straight i with rightwards arrow on top plus straight j with rightwards arrow on top plus 3 straight k with rightwards arrow on top

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D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

tidak ada jawaban yang benar.

tidak ada jawaban yang benar.

Pembahasan

MIsalkan terdapat dua buah titik dan . Vektor AB dapat didefinisikan sebagai: Pada soal diketahui , berdasarkan definisi vektor, maka: Lalu, , berdasarkan definisi vektor, maka: Selanjutnya, . maka vektor adalah: Ditanyakan , substitusi persamaan (ii) dan (iii) sehingga: Dengan demikian, vektor . Oleh karena itu, tidak ada jawaban yang benar.

MIsalkan terdapat dua buah titik straight A open parentheses straight x subscript 1 comma space straight y subscript 1 comma space straight z subscript 1 close parentheses dan straight B open parentheses straight x subscript 2 comma space straight y subscript 2 comma space straight z subscript 2 close parentheses. Vektor AB dapat didefinisikan sebagai:

AB with rightwards arrow on top equals straight B minus straight A equals open parentheses table row cell straight x subscript 2 minus straight x subscript 1 end cell row cell straight y subscript 2 minus straight y subscript 1 end cell row cell straight z subscript 2 minus straight z subscript 1 end cell end table close parentheses

Pada soal diketahui PQ with rightwards arrow on top equals 4 straight i with rightwards arrow on top plus 2 straight k with rightwards arrow on top equals open parentheses table row 4 row 0 row 2 end table close parentheses, berdasarkan definisi vektor, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell PQ with rightwards arrow on top end cell equals cell open parentheses table row 4 row 0 row 2 end table close parentheses end cell row cell straight Q minus straight P end cell equals cell open parentheses table row 4 row 0 row 2 end table close parentheses space... left parenthesis straight i right parenthesis end cell end table

Lalu, PR with rightwards arrow on top equals 2 straight i with rightwards arrow on top plus straight j with rightwards arrow on top plus straight k with rightwards arrow on top equals open parentheses table row 2 row 1 row 1 end table close parentheses, berdasarkan definisi vektor, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell PR with rightwards arrow on top end cell equals cell open parentheses table row 2 row 1 row 1 end table close parentheses end cell row cell straight R minus straight P end cell equals cell open parentheses table row 2 row 1 row 1 end table close parentheses space... left parenthesis ii right parenthesis end cell end table

Selanjutnya, PS with rightwards arrow on top equals negative 1 half PQ with rightwards arrow on top. maka vektor PS with rightwards arrow on top adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell PS with rightwards arrow on top end cell equals cell negative 1 half PQ with rightwards arrow on top end cell row cell straight S minus straight P end cell equals cell negative 1 half open parentheses table row 4 row 0 row 2 end table close parentheses end cell row cell straight S minus straight P end cell equals cell open parentheses table row cell negative 2 end cell row 0 row cell negative 1 end cell end table close parentheses end cell row straight S equals cell open parentheses table row cell negative 2 end cell row 0 row cell negative 1 end cell end table close parentheses plus straight P space... left parenthesis iii right parenthesis end cell end table

Ditanyakan RS with rightwards arrow on top, substitusi persamaan (ii) dan (iii) sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell RS with rightwards arrow on top end cell equals cell straight S minus straight R end cell row blank equals cell open parentheses table row cell negative 2 end cell row 0 row cell negative 1 end cell end table close parentheses plus straight P minus straight R end cell row blank equals cell open parentheses table row cell negative 2 end cell row 0 row cell negative 1 end cell end table close parentheses minus open parentheses straight R minus straight P close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell row 0 row cell negative 1 end cell end table close parentheses minus open parentheses table row 2 row 1 row 1 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 minus 2 end cell row cell 0 minus 1 end cell row cell negative 1 minus 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell row cell negative 1 end cell row cell negative 2 end cell end table close parentheses end cell row blank equals cell negative 4 straight i with rightwards arrow on top minus straight j with rightwards arrow on top minus 2 straight k with rightwards arrow on top end cell end table

Dengan demikian, vektor RS with rightwards arrow on top equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight i with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight j with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight k with rightwards arrow on top end cell end table.

Oleh karena itu, tidak ada jawaban yang benar.

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