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

Pertanyaan

Diketahui undefined dan undefined. Vektor proyeksi ortogonal undefined pada undefined 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  

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

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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