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Diketahui vektor  dan . Proyeksi vektor  pada vekt...

Diketahui vektor bold italic a bold equals bold 2 bold italic i bold plus bold italic j bold minus bold 9 bold italic k bold comma bold space bold italic b bold equals bold italic i bold minus bold italic j bold plus bold 3 bold italic k bold comma bold space bold italic c bold equals bold 3 bold italic i bold plus bold 2 bold italic j bold plus bold italic k dan bold italic d bold equals bold italic a bold plus bold 2 bold italic b. Proyeksi vektor bold italic d pada vektor bold italic c adalah...

  1. 1 half bold italic b 

  2. 1 fourth bold italic d 

  3. 1 half bold italic c 

  4. 1 over 7 bold italic c 

  5. 1 over 7 bold italic b 

Jawaban:

Menentukan vektor bold italic d

table attributes columnalign right center left columnspacing 0px end attributes row bold italic d equals cell bold italic a bold plus bold 2 bold italic b end cell row blank equals cell bold left parenthesis bold 2 bold italic i bold plus bold italic j bold minus bold 9 bold italic k bold right parenthesis bold plus bold 2 bold left parenthesis bold italic i bold minus bold italic j bold plus bold 3 bold italic k bold right parenthesis end cell row blank equals cell bold left parenthesis bold 2 bold italic i bold plus bold italic j bold minus bold 9 bold italic k bold right parenthesis bold plus bold left parenthesis bold 2 bold italic i bold minus bold 2 bold italic j bold plus bold 6 bold italic k bold right parenthesis end cell row blank equals cell bold 4 bold italic i bold minus bold italic j bold minus bold 3 bold italic k end cell end table 

Menentukan proyeksi vektor bold italic d pada vektor bold italic c 

equals fraction numerator bold c bold times bold d over denominator bold vertical line bold c bold vertical line to the power of bold 2 end fraction bold times bold italic c equals fraction numerator left parenthesis 3 times 4 right parenthesis plus left parenthesis 2 times left parenthesis negative 1 right parenthesis right parenthesis plus left parenthesis 1 times left parenthesis negative 3 right parenthesis right parenthesis over denominator left parenthesis square root of 3 squared plus 2 squared plus 1 squared end root right parenthesis squared end fraction bold times bold italic c equals fraction numerator 12 minus 2 minus 3 over denominator left parenthesis square root of 9 plus 4 plus 1 end root right parenthesis squared end fraction bold times bold italic c equals 7 over left parenthesis square root of 14 right parenthesis squared bold times bold italic c equals 7 over 14 bold times bold italic c equals 1 half bold italic c 

Jadi, jawaban yang benar adalah C.

 

 

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