Iklan

Iklan

Pertanyaan

Vektor yang merupakan proyeksi vektor x = 3 i + j ​ − k pada vektor y ​ = 2 i + 5 j ​ + k adalah ...

Vektor yang merupakan proyeksi vektor  pada vektor  adalah ...

  1. stack text i end text with rightwards arrow on top plus 5 over 2 stack text j end text with rightwards arrow on top plus 1 half stack text k end text with rightwards arrow on top 

  2. 2 over 3 stack text i end text with rightwards arrow on top plus 5 over 3 stack text j end text with rightwards arrow on top plus 1 third stack text k end text with rightwards arrow on top 

  3. 1 half stack text i end text with rightwards arrow on top plus 5 over 4 stack text j end text with rightwards arrow on top plus 1 fourth stack text k end text with rightwards arrow on top 

  4. 2 over 5 stack text i end text with rightwards arrow on top minus stack text j end text with rightwards arrow on top minus 1 fifth stack text k end text with rightwards arrow on top 

  5. 1 third stack text i end text with rightwards arrow on top plus 5 over 6 stack text j end text with rightwards arrow on top plus 1 over 6 stack text k end text with rightwards arrow on top 

Iklan

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

jawaban yang tepat adalah B.

Iklan

Pembahasan

Panjang vektor , yaitu Jika vektor dan , maka Proyeksi vektor orthogonal vektor pada dapat ditentukan menggunakan rumus berikut. Berdasarkan konsep tersebut dapat ditentukan penyelesaian soal sebagai berikut. Vektor proyeksi vektor pada adalah Oleh karena itu, jawaban yang tepat adalah B.

Panjang vektor a with rightwards arrow on top equals x i with rightwards arrow on top plus y j with rightwards arrow on top plus z k with rightwards arrow on top, yaitu open vertical bar a with rightwards arrow on top close vertical bar equals square root of x squared plus y squared plus z squared end root

Jika vektor a with rightwards arrow on top equals a subscript 1 i with rightwards arrow on top plus a subscript 2 j with rightwards arrow on top plus a subscript 3 k with rightwards arrow on top dan b with rightwards arrow on top equals b subscript 1 i with rightwards arrow on top plus b subscript 2 j with rightwards arrow on top plus b subscript 3 k with rightwards arrow on top, maka

a with rightwards arrow on top times b with rightwards arrow on top equals a subscript 1 times b subscript 1 plus a subscript 2 times b subscript 2 plus a subscript 3 times b subscript 3

Proyeksi vektor orthogonal vektor a with rightwards arrow on top pada b with rightwards arrow on top dapat ditentukan menggunakan rumus berikut.

c with rightwards arrow on top equals 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 squared end fraction times b with rightwards arrow on top

Berdasarkan konsep tersebut dapat ditentukan penyelesaian soal sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell c with rightwards arrow on top end cell equals cell fraction numerator x with rightwards arrow on top times y with rightwards arrow on top over denominator open vertical bar y with rightwards arrow on top close vertical bar squared end fraction times y with rightwards arrow on top end cell row blank equals cell fraction numerator open parentheses table row 3 row 1 row cell negative 1 end cell end table close parentheses open parentheses table row 2 row 5 row 1 end table close parentheses over denominator open parentheses square root of 2 squared plus 5 squared plus 1 end root close parentheses squared end fraction times open parentheses table row 2 row 5 row 1 end table close parentheses end cell row blank equals cell fraction numerator 3 times 2 plus 1 times 5 plus open parentheses negative 1 close parentheses times 1 over denominator open parentheses square root of 30 close parentheses squared end fraction times open parentheses table row 2 row 5 row 1 end table close parentheses end cell row blank equals cell 10 over 30 times open parentheses table row 2 row 5 row 1 end table close parentheses end cell row blank equals cell 1 third times open parentheses table row 2 row 5 row 1 end table close parentheses end cell row blank equals cell open parentheses table row cell 2 over 3 end cell row cell 5 over 3 end cell row cell 1 third end cell end table close parentheses end cell end table

Vektor proyeksi vektor x with rightwards arrow on top pada y with rightwards arrow on top adalah 2 over 3 i with rightwards arrow on top plus 5 over 3 j with rightwards arrow on top plus 1 third k with rightwards arrow on top 

Oleh karena itu, jawaban yang tepat adalah B.

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

32

Nayla Ainul kifa

Makasih ❤️

Iklan

Iklan

Pertanyaan serupa

Diketahui vektor a = ⎝ ⎛ ​ − 4 − 2 2 ​ ⎠ ⎞ ​ dan b = ⎝ ⎛ ​ 5 − 1 4 ​ ⎠ ⎞ ​ . Proyeksi orthogonal vektor a pada vektor b adalah ...

9

4.5

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

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

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