Roboguru

Apa yang dimaksud dengan skalar? Berikan contohnya!

Pertanyaan

Apa yang dimaksud dengan skalar? Berikan contohnya!

Pembahasan Soal:

Skalar adalah besaran yang hanya memiliki nilai dan tidak memiliki arah. Contohnya adalah semua besaran pokok, energi, kelajuan, usaha, luas, daya, volume, dan lain-lain.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Ayu

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Terakhir diupdate 06 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  dan . Tentukan proyeksi skalar  pada  dan proyeksi skalar  pada

Pembahasan Soal:

Panjang vektor a with rightwards arrow on top dapat ditentukan sebagai berikut.

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 x squared plus y squared plus z squared end root end cell row blank equals cell square root of 3 squared plus 2 squared plus 4 squared end root end cell row blank equals cell square root of 9 plus 4 plus 16 end root end cell row blank equals cell square root of 29 end cell end table

Panjang vektor b with rightwards arrow on top dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar b with rightwards arrow on top close vertical bar end cell equals cell square root of x squared plus y squared plus z squared end root end cell row blank equals cell square root of 0 squared plus 3 squared plus open parentheses negative 4 close parentheses squared end root end cell row blank equals cell square root of 0 plus 9 plus 16 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 end table

Hasil perkalian dari a with rightwards arrow on top times b with rightwards arrow on top adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell open parentheses table row 3 row 2 row 4 end table close parentheses times open parentheses table row 0 row 3 row cell negative 4 end cell end table close parentheses end cell row blank equals cell 3 times 0 plus 2 times 3 plus 4 times open parentheses negative 4 close parentheses end cell row blank equals cell 0 plus 6 minus 16 end cell row blank equals cell negative 10 end cell end table

Proyeksi skalar a with rightwards arrow on top pada b with rightwards arrow on top adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar c with rightwards arrow on top close vertical bar end cell equals cell fraction numerator a with rightwards arrow on top times 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 blank equals cell fraction numerator negative 10 over denominator 5 end fraction end cell row blank equals cell negative 2 end cell end table

Proyeksi skalar b with rightwards arrow on top pada a with rightwards arrow on top adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar c with rightwards arrow on top close vertical bar end cell equals cell fraction numerator a with rightwards arrow on top times b 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 negative 10 over denominator square root of 29 end fraction end cell row blank equals cell fraction numerator negative 10 over denominator square root of 29 end fraction cross times fraction numerator square root of 29 over denominator square root of 29 end fraction end cell row blank equals cell negative 10 over 29 square root of 29 end cell end table

Dengan demikian, proyeksi skalar a with rightwards arrow on top pada b with rightwards arrow on top adalah negative 2 dan proyeksi skalar b with rightwards arrow on top pada a with rightwards arrow on top adalah negative 10 over 29 square root of 29

0

Roboguru

Diketahui  dan . Vektor proyeksi ortogonal  pada  adalah adalah ....

Pembahasan Soal:

Perhatikan bahwa

undefined  
 

Misalkan vektor proyeksi ortogonal undefined pada undefined adalah begin mathsize 14px style p with rightwards arrow on top end style. Oleh karena itu, didapatkan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator open parentheses u with rightwards arrow on top plus v with rightwards arrow on top close parentheses ⋅ v with rightwards arrow on top over denominator open vertical bar v with rightwards arrow on top close vertical bar squared end fraction close parentheses v with rightwards arrow on top end cell equals cell open parentheses fraction numerator open parentheses table row 0 row cell negative sign 9 end cell row 0 end table close parentheses ⋅ open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses over denominator open parentheses square root of 2 squared plus open parentheses negative sign 1 close parentheses squared plus open parentheses negative sign 2 close parentheses squared end root close parentheses squared end fraction close parentheses open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell open parentheses fraction numerator 0 ⋅ 2 plus open parentheses negative sign 9 close parentheses ⋅ open parentheses negative sign 1 close parentheses plus 0 ⋅ open parentheses negative sign 2 close parentheses over denominator open parentheses square root of 4 plus 1 plus 4 end root close parentheses squared end fraction close parentheses open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell open parentheses fraction numerator 0 plus 9 plus 0 over denominator open parentheses square root of 9 close parentheses squared end fraction close parentheses open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell 9 over 9 open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell 2 i with rightwards arrow on top minus sign j with rightwards arrow on top minus sign 2 k with rightwards arrow on top end cell end table end style   
 

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Diketahui vektor  dan vektor , tentukan: b. Proyeksi skalar ortogonal  pada

Pembahasan Soal:

Diketahui:

 a with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 2 row cell negative 2 end cell end table close parentheses
b with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row 3 row 0 end table close parentheses

Proyeksi skalar ortogonal a with rightwards arrow on top pada b with rightwards arrow on top open parentheses open vertical bar c with rightwards arrow on top close vertical bar close parentheses:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar c with rightwards arrow on top close vertical bar end cell equals cell fraction numerator a with rightwards arrow on top times 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 blank equals cell fraction numerator open parentheses table row cell negative 4 end cell row 2 row cell negative 2 end cell end table close parentheses times open parentheses table row cell negative 3 end cell row 3 row 0 end table close parentheses over denominator square root of open parentheses negative 3 close parentheses squared plus 3 squared plus 0 squared end root end fraction end cell row blank equals cell fraction numerator 12 plus 6 plus 0 over denominator square root of 9 plus 9 plus 0 end root end fraction end cell row blank equals cell fraction numerator 18 over denominator square root of 18 end fraction cross times fraction numerator square root of 18 over denominator square root of 18 end fraction end cell row blank equals cell fraction numerator 18 square root of 18 over denominator 18 end fraction end cell row blank equals cell square root of 18 end cell end table 

Jadi, proyeksi skalar ortogonal a with rightwards arrow on top pada b with rightwards arrow on top adalah square root of 18.

0

Roboguru

Diketahui a=(3,2,4) dan b=(0,3,−4). Tentukan proyeksi skalar a pada b dan proyeksi skalar b pada a.

Pembahasan Soal:

Diketahui a=(3,2,4) dan b=(0,3,4).

Ingat!

Rumus proyeksi skalar u dan v:

  • c=vu.v 

Sehingga:

  • Proyeksi skalar a pada b.

capadab=====ba.b02+32+(4)23×0+2×3+4×(4)250+6165102 

  • Proyeksi b pada a.

cbpadaa======aa.b32+22+423×0+2×3+4×(4)290+61629102910×2929291029 

Dengan demikian, proyeksi skalar a pada b adalah 2 dan proyeksi b pada a adalah 291029.

0

Roboguru

Jika vector dan , maka proyeksi scalar orthogonal vector pada vector adalah ...

Pembahasan Soal:

Proyeksi skalar ortogonal suatu vektor pada vektor lain adalah :

  • Proyeksi vektor orthogonal v with rightwards arrow on top pada u with rightwards arrow on top space equals fraction numerator u with rightwards arrow on top times v with rightwards arrow on top over denominator open vertical bar u with rightwards harpoon with barb upwards on top close vertical bar end fraction
  • Proyeksi vektor orthogonal u with rightwards arrow on top pada v with rightwards arrow on top space equals fraction numerator v with rightwards arrow on top times u with rightwards arrow on top over denominator open vertical bar v with rightwards arrow on top close vertical bar end fraction

Diketahui vector u equals left parenthesis 3 comma negative 4 right parenthesis dan v equals left parenthesis 5 comma 2 right parenthesis, cari dulu vector left parenthesis u minus v right parenthesis dan vector u plus v,

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis u minus v right parenthesis end cell equals cell open square brackets table row 3 row cell negative 4 end cell end table close square brackets minus open square brackets table row 5 row 2 end table close square brackets end cell row blank equals cell open square brackets table row cell 3 minus 5 end cell row cell negative 4 minus 2 end cell end table close square brackets end cell row blank equals cell open square brackets table row cell negative 2 end cell row cell negative 6 end cell end table close square brackets end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis u plus v right parenthesis end cell equals cell open square brackets table row 3 row cell negative 4 end cell end table close square brackets plus open square brackets table row 5 row 2 end table close square brackets end cell row blank equals cell open square brackets table row cell 3 plus 5 end cell row cell negative 4 plus 2 end cell end table close square brackets end cell row blank equals cell open square brackets table row 8 row cell negative 2 end cell end table close square brackets end cell end table

Maka di dapatkan u plus v equals left parenthesis 8 comma negative 2 right parenthesis dan u minus v equals left parenthesis negative 2 comma negative 6 right parenthesis.

Proyeksi scalar orthogonal vector left parenthesis u minus v right parenthesis pada vector u plus v,

table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell fraction numerator open parentheses u plus v close parentheses open parentheses u minus v close parentheses over denominator open vertical bar u minus v close vertical bar end fraction end cell row blank equals cell fraction numerator open square brackets table row 8 row cell negative 2 end cell end table close square brackets times open square brackets table row cell negative 2 end cell row cell negative 6 end cell end table close square brackets over denominator square root of left parenthesis negative 2 right parenthesis squared plus left parenthesis negative 6 right parenthesis squared end root end fraction end cell row blank equals cell fraction numerator open square brackets table row cell 8 times negative 2 end cell row cell negative 2 times negative 6 end cell end table close square brackets over denominator square root of 40 end fraction end cell row blank equals cell fraction numerator open square brackets table row cell negative 16 end cell row 12 end table close square brackets over denominator square root of 40 end fraction end cell row blank equals cell fraction numerator open square brackets table row cell negative 16 end cell row 12 end table close square brackets over denominator square root of 4 cross times 10 end root end fraction end cell row blank equals cell fraction numerator open square brackets table row cell negative 16 end cell row 12 end table close square brackets over denominator 2 square root of 10 end fraction end cell row blank equals cell open square brackets table row cell fraction numerator negative 16 over denominator 2 square root of 10 end fraction end cell row cell fraction numerator 12 over denominator 2 square root of 10 end fraction end cell end table close square brackets space rasionalkan end cell row blank equals cell open square brackets table row cell fraction numerator negative 16 over denominator 2 square root of 10 end fraction cross times fraction numerator square root of 10 over denominator square root of 10 end fraction end cell row cell fraction numerator 12 over denominator 2 square root of 10 end fraction cross times fraction numerator square root of 10 over denominator square root of 10 end fraction end cell end table close square brackets end cell row blank equals cell open square brackets table row cell fraction numerator negative 16 square root of 10 over denominator 2 times 10 end fraction end cell row cell fraction numerator 12 square root of 10 over denominator 2 times 10 end fraction end cell end table close square brackets end cell row blank equals cell open square brackets table row cell fraction numerator negative 16 square root of 10 over denominator 20 end fraction end cell row cell fraction numerator 12 square root of 10 over denominator 20 end fraction end cell end table close square brackets space sederhanakan end cell row blank equals cell open square brackets table row cell negative 4 over 5 square root of 10 end cell row cell 3 over 5 square root of 10 end cell end table close square brackets end cell end table


Jadi, proyeksi scalar orthogonal vector left parenthesis u minus v right parenthesis pada vector u plus v adalah open parentheses negative 4 over 5 square root of 10 comma space 3 over 5 square root of 10 close parentheses.

 

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