Roboguru

Jika ,  dan , maka

Pertanyaan

Jika open vertical bar a with rightwards arrow on top close vertical bar equals 1, open vertical bar b with rightwards arrow on top close vertical bar equals 4 dan a with rightwards arrow on top times b with rightwards arrow on top equals 3, maka open vertical bar 2 a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar equals... begin mathsize 14px style space end style 

Pembahasan Soal:

Panjang a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses dapat dituliskan sebagai berikut.

open vertical bar a with rightwards arrow on top close vertical bar equals square root of a subscript 1 squared plus a subscript 2 squared end root 

Berdasarkan yang diketahui, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top close vertical bar end cell equals cell square root of a subscript 1 squared plus a subscript 2 squared end root end cell row 1 equals cell square root of a subscript 1 squared plus a subscript 2 squared end root end cell row cell 1 squared end cell equals cell open parentheses square root of a subscript 1 squared plus a subscript 2 squared end root close parentheses squared end cell row 1 equals cell a subscript 1 squared plus a subscript 2 squared end cell row cell open vertical bar b with rightwards arrow on top close vertical bar end cell equals cell square root of b subscript 1 squared plus b subscript 2 squared end root end cell row 4 equals cell square root of b subscript 1 squared plus b subscript 2 squared end root end cell row cell 4 squared end cell equals cell open parentheses square root of b subscript 1 squared plus b subscript 2 squared end root close parentheses squared end cell row 16 equals cell b subscript 1 squared plus b subscript 2 squared end cell end table 

Jika a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses dan b with rightwards arrow on top equals open parentheses table row cell b subscript 1 end cell row cell b subscript 2 end cell end table close parentheses, maka:

a with rightwards arrow on top times b with rightwards arrow on top equals a subscript 1 b subscript 1 plus a subscript 2 b subscript 2 

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar 2 a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses 2 a subscript 1 minus b subscript 1 close parentheses squared plus open parentheses 2 a subscript 2 minus b subscript 2 close parentheses squared end root end cell row blank equals cell square root of 4 a subscript 1 squared minus 4 a subscript 1 b subscript 1 plus b subscript 1 squared plus 4 a subscript 2 squared minus 4 a subscript 2 b subscript 2 plus b subscript 2 squared end root end cell row blank equals cell square root of 4 open parentheses a subscript 1 squared plus a subscript 2 squared close parentheses minus 4 open parentheses a subscript 1 b subscript 1 plus a subscript 2 b subscript 2 close parentheses plus b subscript 1 squared plus b subscript 2 squared end root end cell row blank equals cell square root of 4 times 1 minus 4 times 3 plus 16 end root end cell row blank equals cell square root of 4 minus 12 plus 16 end root end cell row blank equals cell square root of 8 end cell row blank equals cell square root of 4 times 2 end root end cell row blank equals cell 2 square root of 2 end cell end table 

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open vertical bar 2 a with rightwards arrow on top minus b with rightwards arrow on top close vertical bar end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank 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 square root of 2 end cell end table.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Mahasiswa/Alumni Universitas Indraprasta PGRI

Terakhir diupdate 01 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan yang serupa

Diketahui , , dan . Jika , , dan  merupakan vektor posisi dari A, B, dan C, nyatakan vektor berikut ke dalam bentuk vektor satuan . e.

Pembahasan Soal:

Diketahui A left parenthesis minus sign 2 comma space 1 comma space 3 right parenthesisB left parenthesis minus sign 3 comma space 1 comma space 2 right parenthesis, dan C left parenthesis 3 comma space 2 comma minus sign 1 right parenthesis.

DIberikan a with rightwards arrow on top, b with rightwards arrow on top, dan c with rightwards arrow on top merupakan vektor posisi dari A, B, dan C, maka a with rightwards arrow on top equals negative 2 i with rightwards arrow on top plus j with rightwards arrow on top plus 3 k with rightwards arrow on top, b with rightwards arrow on top equals negative 3 i with rightwards arrow on top plus j with rightwards arrow on top plus 2 k with rightwards arrow on top, dan 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 top. Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell CB with rightwards arrow on top minus 2 stack A C with rightwards arrow on top end cell row blank equals cell open parentheses b with rightwards arrow on top minus c with rightwards arrow on top close parentheses minus 2 open parentheses c with rightwards arrow on top minus a with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses open parentheses table row cell negative 3 end cell row 1 row 2 end table close parentheses minus open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses close parentheses minus 2 open parentheses open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses minus open parentheses table row cell negative 2 end cell row 1 row 3 end table close parentheses close parentheses end cell row blank equals cell open parentheses table row cell negative 6 end cell row cell negative 1 end cell row 3 end table close parentheses minus 2 open parentheses table row 5 row 1 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 6 end cell row cell negative 1 end cell row 3 end table close parentheses minus open parentheses table row 10 row 2 row cell negative 8 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 16 end cell row cell negative 3 end cell row 11 end table close parentheses end cell end table  

Jadi, hasil dari C with B yields on top minus sign 2 AC with rightwards arrow on top dalam vektor satuan adalah negative 16 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus 11 k with rightwards arrow on top.

0

Roboguru

Jika  dan , nilai  adalah ...

Pembahasan Soal:

Tentukan vektor 3 straight u with rightwards arrow on top plus straight v with rightwards arrow on top terlebih dahulu.

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 straight u with rightwards arrow on top plus straight v with rightwards arrow on top end cell equals cell 3 open parentheses table row cell negative 3 end cell row 2 end table close parentheses plus open parentheses table row 5 row cell negative 4 end cell end table close parentheses space end cell row blank equals cell open parentheses table row cell negative 9 end cell row 6 end table close parentheses plus open parentheses table row 5 row cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell row 2 end table close parentheses end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar 3 straight u with rightwards arrow on top plus straight v with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 4 close parentheses squared plus 2 squared end root end cell row blank equals cell square root of 16 plus 4 end root end cell row blank equals cell square root of 20 end cell row blank equals cell 2 square root of 5 end cell end table

Nilai open vertical bar 3 straight u with rightwards arrow on top plus straight v with rightwards arrow on top close vertical bar equals 2 square root of 5.

Jadi, pilihan jawaban yang tepat adalah A.

0

Roboguru

Diketahui koordinat titik  dan . Titik C membagi garis yang melalui titik A dan B di luar dengan perbandingan . Koordinat titik C adalah ...

Pembahasan Soal:

Misalkan, begin mathsize 14px style m space colon space n equals 3 space colon 1 end style.  Dengan menggunakan perbandingan vektor diluar titik maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight C equals cell fraction numerator mB plus open parentheses negative straight n close parentheses straight A over denominator straight m minus straight n end fraction end cell row blank equals cell fraction numerator 3 straight B plus open parentheses negative 1 close parentheses straight A over denominator 3 minus 1 end fraction end cell row blank equals cell fraction numerator 3 straight B minus straight A over denominator 2 end fraction end cell row blank equals cell 1 half open parentheses 3 straight B minus straight A close parentheses end cell row blank equals cell 1 half open parentheses 3 open parentheses table row 0 row 3 end table close parentheses minus open parentheses table row cell negative 4 end cell row 3 end table close parentheses close parentheses end cell row blank equals cell 1 half open parentheses open parentheses table row 0 row 9 end table close parentheses minus open parentheses table row cell negative 4 end cell row 3 end table close parentheses close parentheses end cell row blank equals cell 1 half open parentheses table row 4 row 6 end table close parentheses end cell row blank equals cell open parentheses table row 2 row 3 end table close parentheses end cell end table end style 

Dengan demikian, koordinat titik C adalah begin mathsize 14px style open parentheses 2 comma space 3 close parentheses end style.

1

Roboguru

Diketahui , , dan . Jika , , dan  merupakan vektor posisi dari A, B, dan C, nyatakan vektor berikut ke dalam bentuk vektor satuan . d.

Pembahasan Soal:

Diketahui A left parenthesis minus sign 2 comma space 1 comma space 3 right parenthesisB left parenthesis minus sign 3 comma space 1 comma space 2 right parenthesis, dan C left parenthesis 3 comma space 2 comma minus sign 1 right parenthesis.

DIberikan a with rightwards arrow on top, b with rightwards arrow on top, dan c with rightwards arrow on top merupakan vektor posisi dari A, B, dan C. Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell b with rightwards arrow on top minus a with rightwards arrow on top end cell row blank equals cell open parentheses table row cell negative 3 end cell row 1 row 2 end table close parentheses minus open parentheses table row cell negative 2 end cell row 1 row 3 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row 0 row cell negative 1 end cell end table close parentheses end cell end table  

Jadi, vektor posisi dari stack A B with rightwards arrow on top adalah negative i with rightwards arrow on top minus k with rightwards arrow on top.

0

Roboguru

Diketahui vektor  dan . Panjang vektor

Pembahasan Soal:

Jika diketahui vektor u with rightwards arrow on top equals open parentheses table row x row y end table close parentheses, maka dapat ditentukan panjang vektor u with rightwards arrow on top sebagai berikut.

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

Jika diketahui vektor u with rightwards arrow on top equals open parentheses table row x row y end table close parentheses dan v with rightwards arrow on top equals open parentheses table row a row b end table close parentheses, serta k element of R, maka dapat ditentukan operasi hitung sebagai berikut.

k times u with rightwards arrow on top equals k times open parentheses table row x row y end table close parentheses equals open parentheses table row cell k x end cell row cell k y end cell end table close parentheses

u with rightwards arrow on top plus v with rightwards arrow on top equals open parentheses table row x row y end table close parentheses plus open parentheses table row a row b end table close parentheses equals open parentheses table row cell x plus a end cell row cell y plus b end cell end table close parentheses

Dengan menerapkan operasi penjumlahan dua vektor dan perkalian skalar dengan vektor, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 u with rightwards arrow on top plus v with rightwards arrow on top end cell equals cell 2 open parentheses 4 i with hat on top plus 2 j with hat on top close parentheses plus open parentheses i with hat on top minus 2 j with hat on top close parentheses end cell row blank equals cell open parentheses 8 i with hat on top plus 4 j with hat on top close parentheses plus open parentheses i with hat on top minus 2 j with hat on top close parentheses end cell row blank equals cell 9 i with hat on top plus 2 j with hat on top end cell end table end style 

Dengan menerapkan rumus panjang vektor pada dua dimensi, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar 2 u with rightwards arrow on top plus v with rightwards arrow on top close vertical bar end cell equals cell square root of 9 squared plus 2 squared end root end cell row blank equals cell square root of 81 plus 4 end root end cell row blank equals cell square root of 85 end cell end table end style 

Dengan demikian, panjang vektor begin mathsize 14px style 2 u with rightwards arrow on top plus v with rightwards arrow on top end style adalah begin mathsize 14px style square root of 85 end style satuan.

1

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved