Iklan

Iklan

Pertanyaan

Hitunglah proyeksi skalar ortogonal a pada b dan juga pada dari vektor-vektor berikut. b. a = ( 3 2 ​ ) dan b = ( 2 3 ​ )

Hitunglah proyeksi skalar ortogonal  pada  dan juga begin mathsize 14px style b with rightwards arrow on top end style pada begin mathsize 14px style a with rightwards arrow on top end style dari vektor-vektor berikut.

b.  dan  

  1. ...space 

  2. ...undefined 

Iklan

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Iklan

Pembahasan

Proyeksi skalar ortogonal pada adalah sebagai berikut: Maka, Maka, proyeksi skalar ortogonal pada adalah . Proyeksi skalar ortogonal pada adalah sebagai berikut: Maka, Maka, proyeksi skalarortogonal pada adalah .

Proyeksi skalar ortogonal begin mathsize 14px style a with rightwards arrow on top end style pada begin mathsize 14px style b with rightwards arrow on top end style adalah sebagai berikut:

begin mathsize 14px style vertical line stack O C with rightwards arrow on top vertical line equals vertical line c with rightwards arrow on top vertical line equals fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator vertical line b with rightwards arrow on top vertical line end fraction end style

Maka,

begin mathsize 14px style table attributes columnalign right center left end attributes row cell vertical line c with rightwards arrow on top vertical line end cell equals cell fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator vertical line b with rightwards arrow on top vertical line end fraction end cell row space equals cell fraction numerator left parenthesis 3 cross times 2 right parenthesis plus left parenthesis 2 cross times 3 right parenthesis over denominator square root of 2 squared plus 3 squared end root end fraction end cell row space equals cell fraction numerator 6 plus 6 over denominator square root of 4 plus 9 end root end fraction end cell row space equals cell fraction numerator 12 over denominator square root of 13 end fraction end cell row space equals cell fraction numerator 12 over denominator square root of 13 end fraction cross times fraction numerator square root of 13 over denominator square root of 13 end fraction end cell row space equals cell fraction numerator 12 square root of 13 over denominator 13 end fraction end cell row space space space end table end style 

Maka, proyeksi skalar ortogonal begin mathsize 14px style a with rightwards arrow on top end style pada begin mathsize 14px style b with rightwards arrow on top end style adalah begin mathsize 14px style fraction numerator 12 square root of 13 over denominator 13 end fraction end style.

Proyeksi skalar ortogonal begin mathsize 14px style b with rightwards arrow on top end style pada begin mathsize 14px style a with rightwards arrow on top end style adalah sebagai berikut:

begin mathsize 14px style vertical line stack O D with rightwards arrow on top vertical line equals vertical line d with rightwards arrow on top vertical line equals fraction numerator b with rightwards arrow on top times a with rightwards arrow on top over denominator vertical line a with rightwards arrow on top vertical line end fraction end style

Maka,

begin mathsize 14px style table attributes columnalign center center left end attributes row cell vertical line d with rightwards arrow on top vertical line end cell equals cell fraction numerator b with rightwards arrow on top times a with rightwards arrow on top over denominator vertical line a with rightwards arrow on top vertical line end fraction end cell row space equals cell fraction numerator left parenthesis 2 cross times 3 right parenthesis plus left parenthesis 3 cross times 2 right parenthesis over denominator square root of 3 squared plus 2 squared end root end fraction end cell row space equals cell fraction numerator 6 plus 6 over denominator square root of 9 plus 4 end root end fraction end cell row space equals cell fraction numerator 12 over denominator square root of 13 end fraction end cell row space equals cell fraction numerator 12 over denominator square root of 13 end fraction cross times fraction numerator square root of 13 over denominator square root of 13 end fraction end cell row space equals cell fraction numerator 12 square root of 13 over denominator 13 end fraction end cell end table end style 

Maka, proyeksi skalar ortogonal begin mathsize 14px style b with rightwards arrow on top end style pada begin mathsize 14px style a with rightwards arrow on top end style adalah begin mathsize 14px style fraction numerator 12 square root of 13 over denominator 13 end fraction end style.

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

53

Iklan

Iklan

Pertanyaan serupa

Diketahui vektor a ⇀ = 2 i − 3 j dan b ⇀ = i + j . Proyeksi skalar orthogonal vektor a ⇀ pada b ⇀ adalah…

11

4.0

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

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

[email protected]

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia