Roboguru

Vektor satuan yang searah dengan vektor  adalah ...

Pertanyaan

Vektor satuan yang searah dengan vektor a with rightwards arrow on top equals open parentheses table row 3 row cell negative 4 end cell end table close parentheses adalah ...space 

Pembahasan Soal:

Vektor satuan adalah vektor yang besarnya sama dengan satu dan arahnya sama dengan vektornya. Simbol vektor satuan dituliskan dengan tanda seperti topi (disebut caret) di atas huruf open parentheses a with hat on top close parentheses

Vektor satuan yang searah dengan vektor a with rightwards arrow on top equals open parentheses table row 3 row cell negative 4 end cell end table close parentheses adalah a with hat on top.

Sehingga, a with hat on top:

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 open parentheses table row 3 row cell negative 4 end cell end table close parentheses over denominator square root of 3 squared plus open parentheses negative 4 close parentheses squared end root end fraction end cell row blank equals cell fraction numerator open parentheses table row 3 row cell negative 4 end cell end table close parentheses over denominator square root of 25 end fraction end cell row blank equals cell fraction numerator open parentheses table row 3 row cell negative 4 end cell end table close parentheses over denominator 5 end fraction end cell row blank equals cell 1 fifth open parentheses table row 3 row cell negative 4 end cell end table close parentheses 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 row blank equals cell 3 over 5 i minus 4 over 5 j end cell end table 

Jadi, vektor satuan yang searah dengan vektor a with rightwards arrow on top equals open parentheses table row 3 row cell negative 4 end cell end table close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 3 over 5 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank i 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 4 over 5 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank j 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 . Tentukan panjang vektor PQ, QR, dan PR serta vektor satuan searah dengan vektor PQ.

Pembahasan Soal:

Jika vektor posisi begin mathsize 14px style a with rightwards arrow on top equals left parenthesis x subscript 1 comma space y subscript 1 right parenthesis end style dan begin mathsize 14px style b with rightwards arrow on top equals left parenthesis x subscript 2 comma space y subscript 2 right parenthesis end style, maka panjang vektor adalah

begin mathsize 14px style open vertical bar stack A B with rightwards arrow on top close vertical bar equals square root of open parentheses x subscript 2 minus x subscript 1 close parentheses squared plus open parentheses y subscript 2 minus y subscript 1 close parentheses squared end root end style

Diketahui begin mathsize 14px style P open parentheses negative 1 comma space 2 close parentheses comma space Q open parentheses negative 4 comma space 6 close parentheses comma space R open parentheses 4 comma space 14 close parentheses end style

Panjang vektor PQ adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack P Q with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 4 plus 1 close parentheses squared plus open parentheses 6 minus 2 close parentheses squared end root end cell row blank equals cell square root of 9 plus 16 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 end table end style

Panjang vektor QR adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line stack Q R with rightwards arrow on top vertical line end cell equals cell square root of left parenthesis 4 plus 4 right parenthesis squared plus left parenthesis 14 minus 6 right parenthesis squared end root end cell row blank equals cell square root of 64 plus 64 end root end cell row blank equals cell square root of 128 end cell row blank equals cell 8 square root of 2 end cell end table end style

Panjang vektor PR adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line stack P R with rightwards arrow on top vertical line end cell equals cell square root of left parenthesis 4 plus 1 right parenthesis squared plus left parenthesis 14 minus 2 right parenthesis squared end root end cell row blank equals cell square root of 25 plus 144 end root end cell row blank equals cell square root of 169 end cell row blank equals 13 end table end style

Vektor satuan searah dengan vektor PQ adalah

begin mathsize 14px style e with hat on top equals fraction numerator stack P Q with rightwards arrow on top over denominator open vertical bar stack P Q with rightwards arrow on top close vertical bar end fraction end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell e with hat on top end cell equals cell fraction numerator open parentheses table row cell negative 4 end cell row 6 end table close parentheses minus open parentheses table row cell negative 1 end cell row 2 end table close parentheses over denominator 5 end fraction end cell row blank 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 blank equals cell 1 fifth open parentheses table row cell negative 3 end cell row 4 end table close parentheses end cell end table end style

Dengan demikian, vektor satuan searah dengan vektor PQ adalah begin mathsize 14px style e with hat on top equals open parentheses table row cell negative 3 over 5 end cell row cell 4 over 5 end cell end table close parentheses end style 

Roboguru

Jika , dan , maka vektor satuan adalah ...

Pembahasan Soal:

Vektor satuan dari vektor dua dimensi straight a with rightwards arrow on top equals open parentheses table row cell straight a subscript 1 end cell row cell straight a subscript 2 end cell end table close parentheses adalah sebagai berikut.

fraction numerator straight a with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top close vertical bar end fraction equals fraction numerator open parentheses straight a subscript 1 comma space straight a subscript 2 close parentheses over denominator square root of straight a subscript 1 squared plus straight a subscript 2 squared end root end fraction.

Sebelum mencari vektor satuan dari straight d with rightwards arrow on top, hitunglah operasi vektornya terlebih dahulu, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight d with rightwards arrow on top end cell equals cell 2 straight a with rightwards arrow on top minus 2 straight b with rightwards arrow on top plus straight c with rightwards arrow on top end cell row cell straight d with rightwards arrow on top end cell equals cell 2 open parentheses table row 1 row 5 end table close parentheses minus 2 open parentheses table row 4 row 5 end table close parentheses plus open parentheses table row 0 row 8 end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row 2 row 10 end table close parentheses minus open parentheses table row 8 row 10 end table close parentheses plus open parentheses table row 0 row 8 end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row cell 2 minus 8 plus 0 end cell row cell 10 minus 10 plus 8 end cell end table close parentheses end cell row cell straight d with rightwards arrow on top end cell equals cell open parentheses table row cell negative 6 end cell row 8 end table close parentheses end cell end table

Selanjutnya, vektor satuan straight d with rightwards arrow on top adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight d with rightwards arrow on top over denominator open vertical bar straight d with rightwards arrow on top close vertical bar end fraction end cell equals cell fraction numerator open parentheses negative 6 comma space 8 close parentheses over denominator square root of open parentheses negative 6 close parentheses squared plus 8 squared end root end fraction end cell row blank equals cell fraction numerator open parentheses negative 6 comma space 8 close parentheses over denominator square root of 36 plus 64 end root end fraction end cell row blank equals cell fraction numerator open parentheses negative 6 comma space 8 close parentheses over denominator square root of 100 end fraction end cell row blank equals cell fraction numerator open parentheses negative 6 comma space 8 close parentheses over denominator 10 end fraction end cell row blank equals cell 1 over 10 open parentheses table row cell negative 6 end cell row 8 end table close parentheses end cell end table

Dengan demikian, jawaban yang benar adalah C.

Roboguru

Diketahui koordinat titik , , , dan . Jika hasil dari , maka nilai n adalah ...

Pembahasan Soal:

Ingat bagaimana cara menentukan suatu vektor dengan titik yang diketahui dan ingat operasi perkalian skalar dengan vektor serta operasi penjumlahan dan pengurangan vektor.

Menentukan vektor-vektor

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 minus A end cell row blank equals cell open parentheses 2 , 5 close parentheses minus left parenthesis 4 , 2 right parenthesis end cell row blank equals cell left parenthesis negative 2 , 3 right parenthesis end cell row blank blank blank row cell stack D B with rightwards arrow on top end cell equals cell B minus D end cell row blank equals cell open parentheses 2 , 5 close parentheses minus left parenthesis 8 , 4 right parenthesis end cell row blank equals cell left parenthesis negative 6 , 1 right parenthesis end cell row blank blank blank row cell stack D C with rightwards arrow on top end cell equals cell C minus D end cell row blank equals cell open parentheses 1 , 5 close parentheses minus left parenthesis 8 , 4 right parenthesis end cell row blank equals cell open parentheses negative 7 , 1 close parentheses end cell end table

Menentukan nilai n

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 stack A B with rightwards arrow on top plus 2 stack D B with rightwards arrow on top minus stack D C with rightwards arrow on top end cell equals cell open parentheses table row cell negative n end cell row cell n minus 1 end cell end table close parentheses end cell row cell 3 left parenthesis negative 2 , 3 right parenthesis plus 2 left parenthesis negative 6 , 1 right parenthesis minus open parentheses negative 7 , 1 close parentheses end cell equals cell open parentheses table row cell negative n end cell row cell n minus 1 end cell end table close parentheses end cell row cell 3 open parentheses table row cell negative 2 end cell row 3 end table close parentheses plus 2 open parentheses table row cell negative 6 end cell row 1 end table close parentheses minus open parentheses table row cell negative 7 end cell row 1 end table close parentheses end cell equals cell open parentheses table row cell negative n end cell row cell n minus 1 end cell end table close parentheses end cell row cell open parentheses table row cell negative 6 end cell row 9 end table close parentheses plus open parentheses table row cell negative 12 end cell row 2 end table close parentheses minus open parentheses table row cell negative 7 end cell row 1 end table close parentheses end cell equals cell open parentheses table row cell negative n end cell row cell n minus 1 end cell end table close parentheses end cell row cell open parentheses table row cell negative 18 end cell row 11 end table close parentheses minus open parentheses table row cell negative 7 end cell row 1 end table close parentheses end cell equals cell open parentheses table row cell negative n end cell row cell n minus 1 end cell end table close parentheses end cell row cell open parentheses table row cell negative 11 end cell row 10 end table close parentheses end cell equals cell open parentheses table row cell negative n end cell row cell n minus 1 end cell end table close parentheses end cell end table

dari hasil di atas didapatkan 

table attributes columnalign right center left columnspacing 0px end attributes row cell negative n end cell equals cell negative 11 end cell row n equals 11 end table

Diperoleh n equals 11.

Jadi, dapat disimpulkan bahwa nilai dari n adalah 11.

Oleh karena itu, jawaban yang benar adalah C.

Roboguru

Diketahui , , dan . Jika , maka  ...

Pembahasan Soal:

Diketahui:

Vektor begin mathsize 14px style top enclose a equals 3 top enclose i plus 2 top enclose j end stylebegin mathsize 14px style top enclose b equals top enclose i minus 4 top enclose j end style, dan begin mathsize 14px style top enclose c equals 13 top enclose i plus 4 top enclose j end style.

Jika begin mathsize 14px style top enclose c equals m top enclose a plus n top enclose b end style, sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose c end cell equals cell m top enclose a plus n top enclose b end cell row cell open square brackets table row 13 row 4 end table close square brackets end cell equals cell m open square brackets table row 3 row 2 end table close square brackets plus n open square brackets table row 1 row cell negative 4 end cell end table close square brackets end cell row cell open square brackets table row 13 row 4 end table close square brackets end cell equals cell open square brackets table row cell 3 m end cell row cell 2 m end cell end table close square brackets plus open square brackets table row n row cell negative 4 n end cell end table close square brackets end cell end table end style

Kemudian diperoleh persamaan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 m plus n end cell equals cell 13 space space space... left parenthesis 1 right parenthesis end cell row cell 2 m minus 4 n end cell equals cell 4 space space space space space... left parenthesis 2 right parenthesis end cell end table end style

Gunakan metode eliminasi dan substitusi SPLDV seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell table attributes columnalign center center center end attributes row cell 3 m plus n end cell equals cell 13 space space open vertical bar cross times 2 close vertical bar space end cell row cell 2 m minus 4 n end cell equals cell 4 space space space space open vertical bar cross times 3 close vertical bar space end cell end table bottom enclose table attributes columnalign right center left end attributes row cell 6 m plus 2 n end cell equals 26 row cell 6 m minus 12 n end cell equals cell 12 space minus end cell end table end enclose end cell row blank blank cell space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space table attributes columnalign right center left end attributes row cell space space space space space space space 14 n end cell equals 14 row n equals 1 end table end cell end table end style

Substitusi begin mathsize 14px style n equals 1 end style ke persamaan begin mathsize 14px style open parentheses 1 close parentheses end style seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 m plus n end cell equals 13 row cell 3 m plus 1 end cell equals 13 row cell 3 m end cell equals cell 13 minus 1 end cell row cell 3 m end cell equals 12 row m equals cell 12 over 3 end cell row m equals 4 end table end style

Maka, begin mathsize 14px style m plus n equals 4 plus 1 equals 5 end style.

Roboguru

Vektor satuan dari adalah...

Pembahasan Soal:

Pertama tentukan panjang vektor begin mathsize 14px style open vertical bar p with rightwards arrow on top close vertical bar equals square root of left parenthesis negative 6 right parenthesis squared plus left parenthesis negative 8 right parenthesis squared end root equals 10 end style. Vektor satuan nya adalah  begin mathsize 14px style p with hat on top equals fraction numerator p with rightwards arrow on top over denominator open vertical bar p with rightwards arrow on top close vertical bar end fraction equals fraction numerator negative 6 i minus 8 j over denominator 10 end fraction equals negative 3 over 5 i minus 4 over 5 j end style

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