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

Pertanyaan

Diketahui vektor a with rightwards arrow on top equals negative i minus j plus 2 k space d a n space b with rightwards arrow on top equals i minus j minus 2 k. Proyeksi vektor orthogonal a with rightwards arrow on top pada b with rightwards arrow on top adalah...

  1. negative 1 third i minus 1 third j plus 2 over 3 k

  2. negative 1 third i plus 1 third j plus 2 over 3 k

  3. negative 2 over 3 i plus 2 over 3 j minus 4 over 3 k

  4. negative 2 over 3 i minus 2 over 3 j plus 4 over 3 k

  5. negative 2 over 3 i plus 2 over 3 j plus 4 over 3 k

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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3.6 (3 rating)

Anissa Cyntia Rachman

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Diketahui vektor a=i−2j+k dan vektor b=3i+j−2k. Vektor c mewakili vektor hasil proyeksi orthogonal vektor b pada vektor a, maka vektor c=...

1rb+

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