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

Pertanyaan

Diketahui vektor begin mathsize 14px style a with rightwards arrow on top equals negative i with rightwards arrow on top minus j with rightwards arrow on top plus 2 k with rightwards arrow on top end style dan begin mathsize 14px style b with rightwards arrow on top equals i with rightwards arrow on top minus j with rightwards arrow on top minus 2 k with rightwards arrow on top end style. Proyeksi vektor ortogonal begin mathsize 14px style a with rightwards arrow on top end style pada begin mathsize 14px style b with rightwards arrow on top end style adalah ....

  1. begin mathsize 14px style negative 1 third i with rightwards arrow on top minus 1 third j with rightwards arrow on top plus 2 over 3 k with rightwards arrow on top end style

  2. begin mathsize 14px style negative 1 third i with rightwards arrow on top plus 1 third j with rightwards arrow on top plus 2 over 3 k with rightwards arrow on top end style

  3. begin mathsize 14px style negative 2 over 3 i with rightwards arrow on top plus 2 over 3 j with rightwards arrow on top plus 2 over 3 k with rightwards arrow on top end style

  4. begin mathsize 14px style negative 2 over 3 i with rightwards arrow on top plus 2 over 3 j with rightwards arrow on top minus 4 over 3 k with rightwards arrow on top end style

  5. begin mathsize 14px style negative 2 over 3 i with rightwards arrow on top plus 2 over 3 j with rightwards arrow on top plus 4 over 3 k with rightwards arrow on top end style

Pembahasan:

Diketahui vektor begin mathsize 14px style a with rightwards arrow on top equals negative i with rightwards arrow on top minus j with rightwards arrow on top plus 2 k with rightwards arrow on top end style dan begin mathsize 14px style b with rightwards arrow on top equals i with rightwards arrow on top minus j with rightwards arrow on top minus 2 k with rightwards arrow on top end style

Misal begin mathsize 14px style c with rightwards arrow on top end style adalah proyeksi vektor ortogonal dari begin mathsize 14px style a with rightwards arrow on top end style pada begin mathsize 14px style b with rightwards arrow on top end style, maka kita dapat perhitungan sebagai berikut.

begin mathsize 14px style 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 space. space b with rightwards arrow on top over denominator open vertical bar space 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 left parenthesis negative i with rightwards arrow on top minus j with rightwards arrow on top plus 2 k with rightwards arrow on top right parenthesis. space left parenthesis i with rightwards arrow on top minus j with rightwards arrow on top minus 2 k with rightwards arrow on top right parenthesis over denominator open parentheses square root of 1 squared plus open parentheses negative 1 close parentheses squared plus open parentheses negative 2 close parentheses squared end root close parentheses squared end fraction close parentheses left parenthesis i with rightwards arrow on top minus j with rightwards arrow on top minus 2 k with rightwards arrow on top right parenthesis end cell row blank equals cell open parentheses fraction numerator negative 1 plus 1 minus 4 over denominator 6 end fraction close parentheses left parenthesis i with rightwards arrow on top minus j with rightwards arrow on top minus 2 k with rightwards arrow on top right parenthesis end cell row blank equals cell negative 4 over 6 left parenthesis i with rightwards arrow on top minus j with rightwards arrow on top minus 2 k with rightwards arrow on top right parenthesis end cell row blank equals cell negative 2 over 3 left parenthesis i with rightwards arrow on top minus j with rightwards arrow on top minus 2 k with rightwards arrow on top right parenthesis end cell row blank equals cell negative 2 over 3 i with rightwards arrow on top plus 2 over 3 j with rightwards arrow on top plus 4 over 3 k with rightwards arrow on top end cell end table end style

Jadi, jawabannya adalah E.

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Terakhir diupdate 05 Oktober 2021

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