Pertanyaan

Diketahui vektor a = ⎝ ⎛ − 4 2 − 2 ⎠ ⎞ dan vektor b = ⎝ ⎛ − 3 3 0 ⎠ ⎞ , tentukan: c. Proyeksi vektorortogonal a pada b

Diketahui vektor $a = ⎝ ⎛ - 4 2 - 2 ⎠ ⎞$ dan vektor $b = ⎝ ⎛ - 3 30 ⎠ ⎞$ , tentukan:

c. Proyeksi vektor ortogonal $a$ pada $b$

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E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

proyeksi vektorortogonal pada adalah .

proyeksi vektor ortogonal a with rightwards arrow on top

pada

adalah

open parentheses table row cell negative 3 end cell row 3 row 0 end table close parentheses

Pembahasan

Diketahui: Proyeksi skalar ortogonal pada : Jadi, proyeksi vektorortogonal pada adalah .

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 c with rightwards arrow on top close parentheses :

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

Jadi, proyeksi vektor ortogonal a with rightwards arrow on top pada b with rightwards arrow on top adalah open parentheses table row cell negative 3 end cell row 3 row 0 end table close parentheses .