RoboguruRoboguru
SD

Misalkan P=8i+15j​. a. Carilah ∣∣​P∣∣​ b. Tunjukkan bahwa ∣∣​P∣∣​P​ adalah vektor satuan.

Pertanyaan

Misalkan P with rightwards arrow on top equals 8 i with hat on top plus 15 j with hat on top.

a. Carilah open vertical bar P with rightwards arrow on top close vertical bar

b. Tunjukkan bahwa fraction numerator P with rightwards arrow on top over denominator open vertical bar P with rightwards arrow on top close vertical bar end fraction adalah vektor satuan.

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

terbukti bahwa vektor fraction numerator p with rightwards arrow on top over denominator open vertical bar p with rightwards arrow on top close vertical bar end fraction adalah vektor satuan.

Pembahasan

Panjang vektor a with rightwards arrow on top equals open parentheses table row x row y end table close parentheses dapat ditentukan dengan rumus berikut.

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

Vektor satuan adalah vektor yang panjangnya 1 satuan. Vektor satuan yang searah dengan vektor a with rightwards arrow on top dapat ditentukan dengan rumus berikut.

a with hat on top equals fraction numerator a with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction

Pada soal di atas, misalkan p with rightwards arrow on top equals 8 i with hat on top plus 15 j with hat on top atau dapat dinyatakan dalam bentuk p with rightwards arrow on top equals open parentheses table row 8 row 15 end table close parentheses.

a. Panjang vektor tersebut dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar p with rightwards arrow on top close vertical bar end cell equals cell square root of x squared plus y squared end root end cell row blank equals cell square root of 8 squared plus 15 squared end root end cell row blank equals cell square root of 64 plus 225 end root end cell row blank equals cell square root of 289 end cell row blank equals 17 end table

Dengan demikian, diperoleh open vertical bar p with rightwards arrow on top close vertical bar equals 17 

b. Akan ditunjukkan bahwa fraction numerator p with rightwards arrow on top over denominator open vertical bar p with rightwards arrow on top close vertical bar end fraction adalah vektor satuan.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator p with rightwards arrow on top over denominator open vertical bar p with rightwards arrow on top close vertical bar end fraction end cell equals cell fraction numerator 1 over denominator open vertical bar p with rightwards arrow on top close vertical bar end fraction times p with rightwards arrow on top end cell row blank equals cell 1 over 17 open parentheses table row 8 row 15 end table close parentheses end cell row blank equals cell open parentheses table row cell 8 over 17 end cell row cell 15 over 17 end cell end table close parentheses end cell end table

Panjang vektor fraction numerator p with rightwards arrow on top over denominator open vertical bar p with rightwards arrow on top close vertical bar end fraction dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar fraction numerator p with rightwards arrow on top over denominator open vertical bar p with rightwards arrow on top close vertical bar end fraction close vertical bar end cell equals cell square root of open parentheses 8 over 17 close parentheses squared plus open parentheses 15 over 17 close parentheses squared end root end cell row blank equals cell square root of 64 over 289 plus 225 over 289 end root end cell row blank equals cell square root of 289 over 289 end root end cell row blank equals cell square root of 1 end cell row blank equals 1 end table

Karena vektor tersebut panjangnya 1 satuan sehingga merupakan vektor satuan.

Dengan demikian, terbukti bahwa vektor fraction numerator p with rightwards arrow on top over denominator open vertical bar p with rightwards arrow on top close vertical bar end fraction adalah vektor satuan.

1rb+

4.6 (8 rating)

Mas Rori

Jawaban tidak sesuai

Pertanyaan serupa

Diketahui vektor d=6i−8j, tentukan vektor satuan dari vektor d.

129

5.0

Jawaban terverifikasi

RUANGGURU HQ

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

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia