Roboguru
SD

Jika vektor p​=⎝⎛​2x−3​⎠⎞​, vektor q​=⎝⎛​42−4​⎠⎞​, dan vektor proyeksi p​ pada q​ adalah r=98​i+94​j​−98​k, maka nilai x2 adalah ....

Pertanyaan

Jika vektor p with rightwards arrow on top equals open parentheses table row 2 row x row cell negative 3 end cell end table close parentheses, vektor q with rightwards arrow on top equals open parentheses table row 4 row 2 row cell negative 4 end cell end table close parentheses, dan vektor proyeksi p with rightwards arrow on top pada q with rightwards arrow on top adalah r with rightwards arrow on top equals 8 over 9 i with rightwards arrow on top plus 4 over 9 j with rightwards arrow on top minus 8 over 9 k with rightwards arrow on top, maka nilai x squared adalah ....

  1. 25space 

  2. 64space 

  3. 49space 

  4. 81space 

  5. 36space 

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Dengan menerapkan rumus proyeksi ortogonal vektor, diperoleh perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell r with rightwards arrow on top end cell equals cell open parentheses fraction numerator p with rightwards arrow on top times q with rightwards arrow on top over denominator open vertical bar q with rightwards arrow on top close vertical bar squared end fraction close parentheses times q with rightwards arrow on top end cell row cell open parentheses table row cell 8 over 9 end cell row cell 4 over 9 end cell row cell fraction numerator negative 8 over denominator 9 end fraction end cell end table close parentheses end cell equals cell open parentheses fraction numerator 2 times 4 plus x times 2 plus open parentheses negative 3 close parentheses open parentheses negative 4 close parentheses over denominator 4 squared plus 2 squared plus open parentheses negative 4 close parentheses squared end fraction close parentheses open parentheses table row 4 row 2 row cell negative 4 end cell end table close parentheses end cell row cell open parentheses table row cell 8 over 9 end cell row cell 4 over 9 end cell row cell fraction numerator negative 8 over denominator 9 end fraction end cell end table close parentheses end cell equals cell open parentheses fraction numerator 8 plus 2 x plus 12 over denominator 16 plus 4 plus 16 end fraction close parentheses open parentheses table row 4 row 2 row cell negative 4 end cell end table close parentheses end cell row cell 2 over 9 up diagonal strike open parentheses table row 4 row 2 row cell negative 4 end cell end table close parentheses end strike end cell equals cell fraction numerator 20 plus 2 x over denominator 36 end fraction up diagonal strike open parentheses table row 4 row 2 row cell negative 4 end cell end table close parentheses end strike end cell row cell 2 over 9 end cell equals cell fraction numerator 20 plus 2 x over denominator 36 end fraction end cell row cell 180 plus 18 x end cell equals 72 row cell 18 x end cell equals cell 72 minus 180 end cell row blank equals cell negative 108 end cell row x equals cell negative 6 end cell row cell x squared end cell equals cell open parentheses negative 6 close parentheses squared end cell row blank equals 36 end table 

Jadi, nilai x squared adalah 36.

Dengan demikian, jawaban yang tepat adalah E.

34

0.0 (0 rating)

Pertanyaan serupa

Proyeksi vektor , pada vektor b ⃗yang sejajar tetapi berlawanan arah dengan vektor (1,-2,-2) adalah vektor z ⃗. Maka koordinat vektor  adalah ...

53

0.0

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

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia