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Pertanyaan

Diketahui vektor a = ⎝ ⎛ ​ − 1 − 3 2 ​ ⎠ ⎞ ​ dan b = ⎝ ⎛ ​ − 2 6 1 ​ ⎠ ⎞ ​ . Vektor proyeksi ortogonal dari vektor b pada vektor a adalah ....

Diketahui vektor  dan . Vektor proyeksi ortogonal dari vektor  pada vektor  adalah ....

  1. begin mathsize 14px style negative sign 2 i with rightwards arrow on top plus 6 j with rightwards arrow on top plus k with rightwards arrow on top end style 

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

  3. begin mathsize 14px style 2 i with rightwards arrow on top plus 6 j with rightwards arrow on top minus sign 4 k with rightwards arrow on top end style 

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

  5. begin mathsize 14px style 2 i with rightwards arrow on top minus sign 6 j with rightwards arrow on top minus sign k with rightwards arrow on top end style 

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

jawaban yang tepat adalah D.

Pembahasan

Misalkan vektor proyeksi ortogonal dari vektor terhadap vektor adalah .Oleh karena itu, didapatkan bahwa Jadi, jawaban yang tepat adalah D.

Misalkan vektor proyeksi ortogonal dari vektor undefined terhadap vektor undefined adalah undefined. Oleh karena itu, didapatkan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p with rightwards arrow on top end cell equals cell open parentheses fraction numerator a with rightwards arrow on top ⋅ b with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar squared end fraction close parentheses a with rightwards arrow on top end cell row blank equals cell open parentheses fraction numerator open parentheses table row cell negative sign 1 end cell row cell negative sign 3 end cell row 2 end table close parentheses ⋅ open parentheses table row cell negative sign 2 end cell row 6 row 1 end table close parentheses over denominator open parentheses square root of open parentheses negative sign 1 close parentheses squared plus open parentheses negative sign 3 close parentheses squared plus 2 squared end root close parentheses squared end fraction close parentheses open parentheses table row cell negative sign 1 end cell row cell negative sign 3 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses fraction numerator open parentheses negative sign 1 close parentheses ⋅ open parentheses negative sign 2 close parentheses plus open parentheses negative sign 3 close parentheses ⋅ 6 plus 2 ⋅ 1 over denominator open parentheses square root of 1 plus 9 plus 4 end root close parentheses squared end fraction close parentheses open parentheses table row cell negative sign 1 end cell row cell negative sign 3 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses fraction numerator 2 minus sign 18 plus 2 over denominator open parentheses square root of 14 close parentheses squared end fraction close parentheses open parentheses table row cell negative sign 1 end cell row cell negative sign 3 end cell row 2 end table close parentheses end cell row blank equals cell fraction numerator negative sign 14 over denominator 14 end fraction open parentheses table row cell negative sign 1 end cell row cell negative sign 3 end cell row 2 end table close parentheses end cell row blank equals cell negative sign open parentheses table row cell negative sign 1 end cell row cell negative sign 3 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses table row 1 row 3 row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell i with rightwards arrow on top plus 3 j with rightwards arrow on top minus sign 2 k with rightwards arrow on top end cell end table end style

Jadi, jawaban yang tepat adalah D.

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