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Pertanyaan

Diketahui dan .Vektor proyeksi ortogonal pada v adalah adalah ....

Diketahui undefined dan undefined. Vektor proyeksi ortogonal undefined pada  adalah adalah ....

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

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

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

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

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

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

jawaban yang tepat adalah C.

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Pembahasan

Perhatikan bahwa Misalkan vektor proyeksi ortogonal pada adalah .Oleh karena itu, didapatkan bahwa Jadi, jawaban yang tepat adalah C.

Perhatikan bahwa

undefined  
 

Misalkan vektor proyeksi ortogonal undefined pada undefined adalah begin mathsize 14px style p with rightwards arrow on top end style. Oleh karena itu, didapatkan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator open parentheses u with rightwards arrow on top plus v with rightwards arrow on top close parentheses ⋅ v with rightwards arrow on top over denominator open vertical bar v with rightwards arrow on top close vertical bar squared end fraction close parentheses v with rightwards arrow on top end cell equals cell open parentheses fraction numerator open parentheses table row 0 row cell negative sign 9 end cell row 0 end table close parentheses ⋅ open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses over denominator open parentheses square root of 2 squared plus open parentheses negative sign 1 close parentheses squared plus open parentheses negative sign 2 close parentheses squared end root close parentheses squared end fraction close parentheses open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell open parentheses fraction numerator 0 ⋅ 2 plus open parentheses negative sign 9 close parentheses ⋅ open parentheses negative sign 1 close parentheses plus 0 ⋅ open parentheses negative sign 2 close parentheses over denominator open parentheses square root of 4 plus 1 plus 4 end root close parentheses squared end fraction close parentheses open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell open parentheses fraction numerator 0 plus 9 plus 0 over denominator open parentheses square root of 9 close parentheses squared end fraction close parentheses open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell 9 over 9 open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell 2 i with rightwards arrow on top minus sign 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 C.

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

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