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Diketahui segitiga PQR, dengan P(0, 5, 4), Q(3, 0, 1), dan R(4, 1, 0). Titik S pada PR sehingga PS=41​PR. Panjang QS​= ....

Pertanyaan

Diketahui segitiga PQR, dengan straight P open parentheses 0 comma space 5 comma space 4 close parenthesesstraight Q open parentheses 3 comma space 0 comma space 1 close parentheses, dan straight R open parentheses 4 comma space 1 comma space 0 close parentheses. Titik straight S pada PR sehingga PS with rightwards arrow on top equals 1 fourth PR with rightwards arrow on top. Panjang QS with rightwards arrow on top equals ....

  1. 2 square root of 6

  2. 2 square root of 11

  3. 2 square root of 14

  4. 4 square root of 6

  5. 4 square root of 11

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah A.

Ingat!

  • Jika koordinat titik straight A open parentheses x subscript 1 comma space y subscript 1 close parentheses dan straight B open parentheses x subscript 2 comma space y subscript 2 close parentheses maka dapat ditetapkan:

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

  • Rumus untuk menentukan penjumlahan dan pengurangan dua vektor, jika diketahui a with rightwards arrow on top equals open parentheses table row cell x subscript 1 end cell row cell y subscript 1 end cell end table close parentheses dan vektor b with rightwards arrow on top equals open parentheses table row cell x subscript 2 end cell row cell y subscript 2 end cell end table close parentheses maka

a with rightwards arrow on top plus-or-minus b with rightwards arrow on top equals open parentheses table row cell x subscript 1 end cell row cell y subscript 1 end cell end table close parentheses plus-or-minus open parentheses table row cell x subscript 2 end cell row cell y subscript 2 end cell end table close parentheses equals open parentheses table row cell x subscript 1 plus-or-minus x subscript 2 end cell row cell y subscript 1 plus-or-minus y subscript 2 end cell end table close parentheses

  • Rumus untuk menentukan panjang vektor r with rightwards arrow on top equals open parentheses table row x row y row z end table close parentheses adalah sebagai  berikut:

open vertical bar r with rightwards arrow on top close vertical bar equals square root of x squared plus y squared plus z squared end root 

  • Rumus untuk perkalian skalar m dengan vektor a with rightwards arrow on top equals open parentheses table row cell x subscript 1 end cell row cell y subscript 1 end cell end table close parentheses adalah sebagai berikut:

m a with rightwards arrow on top equals m open parentheses table row cell x subscript 1 end cell row cell x subscript 2 end cell end table close parentheses equals open parentheses table row cell m x subscript 1 end cell row cell m x subscript 2 end cell end table close parentheses 

Diketahui:

straight P open parentheses 0 comma space 5 comma space 4 close parentheses rightwards arrow P with rightwards arrow on top equals open parentheses table row 0 row 5 row 4 end table close parentheses 

straight Q open parentheses 3 comma space 0 comma space 1 close parentheses rightwards arrow Q with rightwards arrow on top equals open parentheses table row 3 row 0 row 1 end table close parentheses

straight R open parentheses 4 comma space 1 comma space 0 close parentheses rightwards arrow R with rightwards arrow on top equals open parentheses table row 4 row 1 row 0 end table close parentheses 

Titik straight S pada PR sehingga stack P S with rightwards arrow on top equals 1 fourth stack P R with rightwards arrow on top.

Ditanya: panjang stack Q S with rightwards arrow on top.

Jawab:

Panjang vektor S with rightwards arrow on top adalah sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell stack P S with rightwards arrow on top end cell equals cell 1 fourth stack P R with rightwards arrow on top end cell row cell S with rightwards arrow on top minus P with rightwards arrow on top end cell equals cell 1 fourth open parentheses R with rightwards arrow on top minus P with rightwards arrow on top close parentheses end cell row cell S with rightwards arrow on top end cell equals cell 1 fourth open parentheses R with rightwards arrow on top minus P with rightwards arrow on top close parentheses plus P with rightwards arrow on top end cell row blank equals cell 1 fourth open parentheses open parentheses table row 4 row 1 row 0 end table close parentheses minus open parentheses table row 0 row 5 row 4 end table close parentheses close parentheses plus open parentheses table row 0 row 5 row 4 end table close parentheses end cell row blank equals cell 1 fourth open parentheses table row 4 row cell negative 4 end cell row cell negative 4 end cell end table close parentheses plus open parentheses table row 0 row 5 row 4 end table close parentheses end cell row blank equals cell open parentheses table row 1 row cell negative 1 end cell row cell negative 1 end cell end table close parentheses plus open parentheses table row 0 row 5 row 4 end table close parentheses end cell row blank equals cell open parentheses table row 1 row 4 row 3 end table close parentheses end cell end table 

Dengan demikian, panjang vektor stack Q S with rightwards arrow on top adalah sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack Q S with rightwards arrow on top close vertical bar end cell equals cell open vertical bar S with rightwards arrow on top minus Q with rightwards arrow on top close vertical bar end cell row blank equals cell square root of open parentheses 1 minus 3 close parentheses squared plus open parentheses 4 minus 0 close parentheses squared plus open parentheses 3 minus 1 close parentheses squared end root end cell row blank equals cell square root of open parentheses negative 2 close parentheses squared plus 4 squared plus 2 squared end root end cell row blank equals cell square root of 4 plus 16 plus 4 end root end cell row blank equals cell square root of 24 end cell row blank equals cell square root of 4 cross times 6 end root end cell row blank equals cell 2 square root of 6 end cell end table 

Oleh karena itu, jawaban yang benar adalah A.

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Pembahasan lengkap banget Makasih ❤️

Pertanyaan serupa

Dengan menggunakan vektor a, vektor b, dan vektor c pada soal Nomor 1, tentukanlah: d. ∣∣​p​∣∣​  e. ∣∣​q​∣∣​  f. ∣∣​r∣∣​

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