Diketahui vektor a=−i−j+2k dan b=i−j−2k. Proyeksi vektor orthogonal a pada b adalah...

Pertanyaan

Diketahui vektor $\overrightarrow a=-i-j+2k\;dan\;\overrightarrow b=i-j-2k.$ Proyeksi vektor orthogonal $\overrightarrow a$ pada $\overrightarrow b$ adalah...

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

$P r o y e k s i space v e k t o r space o r t h o g o n a l space a with rightwards arrow on top space p a d a space b with rightwards arrow on top comma space m i s a l k a n space c with rightwards arrow on top c with ⃗ on top equals fraction numerator a with ⃗ on top straight space. b with ⃑ on top over denominator open vertical bar b with ⃑ on top close vertical bar squared end fraction. b with ⃑ on top equals fraction numerator open parentheses table row cell negative 1 end cell row cell negative 1 end cell row 2 end table close parentheses straight space. open parentheses table row 1 row cell negative 1 end cell row cell negative 2 end cell end table close parentheses over denominator open parentheses 1 close parentheses squared plus open parentheses negative 1 close parentheses squared plus open parentheses negative 2 close parentheses squared end fraction. open parentheses table row 1 row cell negative 1 end cell row cell negative 2 end cell end table close parentheses equals fraction numerator open parentheses negative 1 close parentheses. open parentheses 1 close parentheses plus open parentheses negative 1 close parentheses. open parentheses negative 1 close parentheses plus 2 open parentheses negative 2 close parentheses over denominator 6 end fraction. open parentheses table row 1 row cell negative 1 end cell row cell negative 2 end cell end table close parentheses equals fraction numerator negative 4 over denominator 6 end fraction open parentheses table row 1 row cell negative 1 end cell row cell negative 2 end cell end table close parentheses c with ⃗ on top equals negative 2 over 3 open parentheses table row 1 row cell negative 1 end cell row cell negative 2 end cell end table close parentheses space a t a u space c with ⃗ on top equals negative 2 over 3 i plus 2 over 3 j plus 4 over 3 k$

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