Roboguru

Tentukan vektor satuan dari vektor-vektor berikut!  b.

Pertanyaan

Tentukan vektor satuan dari vektor-vektor berikut! 

b. begin mathsize 14px style straight b with rightwards arrow on top equals open parentheses table row 9 row cell negative 8 end cell end table close parentheses end style  

Pembahasan Video:

Pembahasan Soal:

menentukan panjang vektor undefined    

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight b with rightwards arrow on top end cell equals cell open parentheses table row 9 row cell negative 8 end cell end table close parentheses end cell row cell vertical line straight b with rightwards arrow on top vertical line end cell equals cell square root of left parenthesis 9 right parenthesis squared plus left parenthesis negative 8 right parenthesis squared end root end cell row blank equals cell square root of 81 plus 64 end root end cell row blank equals cell square root of 145 end cell end table end style  

vektor satuan dari undefined adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight b with hat on top end cell equals cell fraction numerator 1 over denominator vertical line straight b with rightwards arrow on top vertical line end fraction cross times straight b with rightwards arrow on top end cell row blank equals cell fraction numerator 1 over denominator square root of 145 end fraction cross times open parentheses table row 9 row cell negative 8 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator 9 over denominator square root of 145 end fraction end cell row cell negative fraction numerator 8 over denominator square root of 145 end fraction end cell end table close parentheses end cell end table end style  

Jadi vektor satuan dari undefined adalah

 begin mathsize 14px style straight b with hat on top equals open parentheses table row cell fraction numerator 9 over denominator square root of 145 end fraction end cell row cell negative fraction numerator 8 over denominator square root of 145 end fraction end cell end table close parentheses end style 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

D. Entry

Terakhir diupdate 07 Juni 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 vektor-vektor: Tentukan vektor satuan dari  !

Pembahasan Soal:

Ingat bahwa vektor satuan adalah vektor yang panjangnya sama dengan satu. Berdasarkan soal diketahui straight a with rightwards arrow on top equals open parentheses table row 6 row 0 end table close parentheses comma space straight b with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row cell negative 4 end cell end table close parentheses comma space straight c with rightwards arrow on top equals open parentheses table row 5 row 2 end table close parentheses comma space dan space straight d with rightwards arrow on top equals open parentheses table row 4 row cell negative 1 end cell end table close parentheses, sehingga panjang vektor 1 third straight b with rightwards arrow on top minus 2 straight c with rightwards arrow on top plus 5 straight d with rightwards arrow on top:

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 third straight b with rightwards arrow on top minus 2 straight c with rightwards arrow on top plus 5 straight d with rightwards arrow on top end cell equals cell 1 third open parentheses table row cell negative 3 end cell row cell negative 4 end cell end table close parentheses minus 2 open parentheses table row 5 row 2 end table close parentheses plus 5 open parentheses table row 4 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row cell fraction numerator negative 4 over denominator 3 end fraction end cell end table close parentheses minus open parentheses table row 10 row 4 end table close parentheses plus open parentheses table row 20 row cell negative 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row 9 row cell fraction numerator negative 4 minus 12 minus 15 over denominator 3 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row 9 row cell fraction numerator negative 31 over denominator 3 end fraction end cell end table close parentheses end cell row cell open vertical bar 1 third straight b minus 2 straight c plus 5 straight d close vertical bar end cell equals cell square root of 9 squared plus open parentheses fraction numerator negative 31 over denominator 3 end fraction close parentheses squared end root end cell row blank equals cell square root of 81 plus 961 over 9 end root end cell row blank equals cell square root of fraction numerator 243 plus 961 over denominator 9 end fraction end root end cell row blank equals cell square root of fraction numerator 1.204 over denominator 9 end fraction end root end cell row blank equals cell 2 square root of 301 over 9 end root end cell row blank equals cell 2 over 3 square root of 301 end cell end table


Jadi, vektor satuan 2 straight a with rightwards arrow on top minus straight c with rightwards arrow on top minus straight d with rightwards arrow on top:

table attributes columnalign right center left columnspacing 0px end attributes row cell vektor space satuan space 1 third straight b with rightwards arrow on top minus 2 straight c with rightwards arrow on top plus 5 straight d with rightwards arrow on top end cell equals cell fraction numerator 1 over denominator open vertical bar begin display style 1 third straight b minus 2 straight c plus 5 straight d end style close vertical bar end fraction times open parentheses 1 third straight b with rightwards arrow on top minus 2 straight c with rightwards arrow on top plus 5 straight d with rightwards arrow on top close parentheses end cell row blank equals cell fraction numerator 1 over denominator 2 over 3 square root of 301 end fraction open parentheses table row 9 row cell fraction numerator negative 31 over denominator 3 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator 27 over denominator 2 square root of 301 end fraction end cell row cell fraction numerator negative 93 over denominator 6 square root of 301 end fraction end cell end table close parentheses end cell end table

0

Roboguru

Diketahui koordinat titik  dan . Tentukan vektor satuan yang searah dengan vektor

Pembahasan Soal:

Titik begin mathsize 14px style straight A open parentheses 1 comma negative 6 close parentheses end style dan begin mathsize 14px style straight B open parentheses negative 5 comma 2 close parentheses end style, sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards arrow on top end cell equals cell straight B minus straight A end cell row blank equals cell open parentheses table row 1 row cell negative 6 end cell end table close parentheses minus open parentheses table row cell negative 5 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses table row 6 row cell negative 8 end cell end table close parentheses end cell end table end style

Vektor satuan yang searah dengan stack A B with rightwards arrow on top yaitu

 table attributes columnalign right center left columnspacing 0px end attributes row cell e subscript stack A B with rightwards arrow on top end subscript end cell equals cell fraction numerator AB with rightwards arrow on top over denominator stack open vertical bar AB close vertical bar with rightwards arrow on top end fraction end cell row blank equals cell fraction numerator open parentheses table row 6 row cell negative 8 end cell end table close parentheses over denominator square root of 6 squared plus open parentheses negative 8 close parentheses squared end root end fraction end cell row blank equals cell fraction numerator open parentheses table row 6 row cell negative 8 end cell end table close parentheses over denominator square root of 100 end fraction end cell row blank equals cell fraction numerator open parentheses table row 6 row cell negative 8 end cell end table close parentheses over denominator 10 end fraction end cell row blank equals cell open parentheses table row cell 3 over 5 end cell row cell negative 4 over 5 end cell end table close parentheses end cell end table

Jadi, vektor satuan yang searah dengan begin mathsize 14px style open vertical bar AB with rightwards arrow on top close vertical bar end style adalah begin mathsize 14px style open parentheses table row cell 3 over 5 end cell row cell negative 4 over 5 end cell end table close parentheses end style.

0

Roboguru

Tentukan vektor satuan dari vektor-vektor berikut!  a.

Pembahasan Soal:

Jika diketahui vektor a with rightwards arrow on top equals open parentheses table row x row y end table close parentheses, maka vektor satuan dari a with rightwards arrow on top dapat ditentukan dengan rumus berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with hat on top end cell equals cell fraction numerator a with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of x squared plus y squared end root end fraction times open parentheses table row x row y end table close parentheses end cell end table

Panjang vektor undefined di atas adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top end cell equals cell i with rightwards arrow on top minus j with rightwards arrow on top end cell row cell open vertical bar straight a with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses 1 close parentheses squared plus open parentheses negative 1 close parentheses squared end root end cell row blank equals cell square root of 1 plus 1 end root end cell row blank equals cell square root of 2 end cell end table 

Vektor satuan dari begin mathsize 14px style straight a with rightwards arrow on top end style adalah 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with hat on top end cell equals cell fraction numerator 1 over denominator open vertical bar straight a with rightwards arrow on top close vertical bar end fraction times straight a with rightwards arrow on top end cell row blank equals cell fraction numerator 1 over denominator square root of 2 end fraction times open parentheses table row 1 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator 1 over denominator square root of 2 end fraction end cell row cell negative fraction numerator 1 over denominator square root of 2 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 half square root of 2 end cell row cell negative 1 half square root of 2 end cell end table close parentheses end cell end table 

Dengan demikian, vektor satuan dari begin mathsize 14px style straight a with rightwards arrow on top end style adalah straight a with hat on top equals 1 half square root of 2 i with rightwards arrow on top minus 1 half square root of 2 j with rightwards arrow on top.

0

Roboguru

Diketahui vektor , , dan b. Tentukan vektor sauan dari vektor , vektor  dan vektor

Pembahasan Soal:

Untuk menyelesaikan soal di atas dapat kita selesaikan dengan menggunakan rumus:

begin mathsize 14px style a 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 end style 

Pertama kita menentukan panjang dari masing-masing vektor di atas:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell vertical line a with rightwards arrow on top vertical line end cell end table equals square root of open parentheses a subscript 1 close parentheses squared plus open parentheses a subscript 2 close parentheses squared plus open parentheses a subscript 3 close parentheses squared plus... plus open parentheses a subscript n close parentheses squared end root comma space maka end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line straight a with rightwards arrow on top vertical line end cell equals cell square root of open parentheses negative 3 close parentheses squared plus open parentheses 4 close parentheses squared end root end cell row cell vertical line straight a with rightwards arrow on top vertical line end cell equals cell square root of 9 plus 16 end root end cell row cell vertical line straight a with rightwards arrow on top vertical line end cell equals cell square root of 25 end cell row cell vertical line straight a with rightwards arrow on top vertical line end cell equals 5 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line b with rightwards arrow on top vertical line end cell equals cell square root of open parentheses 2 close parentheses squared plus open parentheses 3 close parentheses squared end root end cell row cell vertical line b with rightwards arrow on top vertical line end cell equals cell square root of 4 plus 9 end root end cell row cell vertical line b with rightwards arrow on top vertical line end cell equals cell square root of 13 end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line c with rightwards arrow on top vertical line end cell equals cell square root of left parenthesis negative 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root end cell row cell vertical line c with rightwards arrow on top vertical line end cell equals cell square root of 5 end cell end table end style

Maka vektor satuannya adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row a equals cell fraction numerator a with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction end cell row a equals cell fraction numerator open parentheses table row cell negative 3 end cell row 4 end table close parentheses over denominator 5 end fraction end cell row a equals cell 1 fifth open parentheses table row cell negative 3 end cell row 4 end table close parentheses end cell row a equals cell open parentheses table row cell bevelled fraction numerator negative 3 over denominator 5 end fraction end cell row cell bevelled 4 over 5 end cell end table close parentheses end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row b equals cell fraction numerator b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar end fraction end cell row b equals cell fraction numerator open parentheses table row 2 row 3 end table close parentheses over denominator square root of 13 end fraction end cell row b equals cell fraction numerator 1 over denominator square root of 13 end fraction open parentheses table row 2 row 3 end table close parentheses end cell row b equals cell open parentheses table row cell bevelled fraction numerator 2 over denominator square root of 13 end fraction end cell row cell bevelled fraction numerator 3 over denominator square root of 13 end fraction end cell end table close parentheses end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row c equals cell fraction numerator c with rightwards arrow on top over denominator vertical line c with rightwards arrow on top vertical line end fraction end cell row b equals cell fraction numerator blank over denominator square root of 5 end fraction end cell row b equals cell fraction numerator 1 over denominator square root of 5 end fraction open parentheses table row cell negative 1 end cell row 2 end table close parentheses end cell row b equals cell open parentheses table row cell bevelled fraction numerator negative 1 over denominator square root of 5 end fraction end cell row cell bevelled fraction numerator 2 over denominator square root of 5 end fraction end cell end table close parentheses end cell end table end style

 

0

Roboguru

Diketahui titik  dan . Jika  adalah vektor satuan dari , nilai dari

Pembahasan Soal:

Diketahui titik begin mathsize 14px style straight D open parentheses 6 comma negative 5 close parentheses end style dan begin mathsize 14px style straight E open parentheses negative 2 comma 1 close parentheses end style. Jika begin mathsize 14px style straight e with rightwards harpoon with barb upwards on top end style adalah vektor satuan dari begin mathsize 14px style ED with rightwards arrow on top end style, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell ED with rightwards arrow on top end cell equals cell straight d with rightwards arrow on top minus straight e with rightwards arrow on top end cell row blank equals cell open parentheses table row 6 row cell negative 5 end cell end table close parentheses minus open parentheses table row cell negative 2 end cell row 1 end table close parentheses end cell row blank equals cell open parentheses table row 8 row cell negative 6 end cell end table close parentheses end cell end table  

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar ED close vertical bar end cell equals cell square root of 8 squared plus open parentheses negative 6 close parentheses squared end root end cell row blank equals cell square root of 64 plus 36 end root end cell row blank equals cell square root of 100 end cell row blank equals 10 end table end style 

Sehingga vektor satuan dari begin mathsize 14px style ED with rightwards arrow on top end style adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight e with rightwards harpoon with barb upwards on top end cell equals cell fraction numerator 1 over denominator open vertical bar ED with rightwards arrow on top close vertical bar end fraction times ED with rightwards arrow on top space end cell row blank equals cell 1 over 10 times open parentheses table row 8 row cell negative 6 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 8 over 10 end cell row cell negative 6 over 10 end cell end table close parentheses end cell row cell straight e with rightwards harpoon with barb upwards on top end cell equals cell open parentheses table row cell 4 over 5 end cell row cell negative 3 over 5 end cell end table close parentheses end cell end table end style 

Jadi jawaban yang tepat adalah B 

0

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