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Perhatikan gambar berikut.     Proyeksi vektor ...

Perhatikan gambar berikut.
 


 

Proyeksi vektor AB with bar on top pada AC with bar on top adalah ....

  1. AD with bar on top 

  2. AE with bar on top 

  3. BC with bar on top 

  4. BD with bar on top 

  5. BE with bar on top 

Jawaban:

Proyeksi ortogonal vektor a with rightwards arrow on top pada vektor b with rightwards arrow on top.

Proyeksi space vektor equals open parentheses fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar squared end fraction close parentheses times b with rightwards arrow on top

Akan ditentukan proyeksi vektor AB with bar on top pada AC with bar on top, yaitu

Proyeksi space vektor equals open parentheses fraction numerator AB with rightwards arrow on top times AC with rightwards arrow on top over denominator open vertical bar AC with rightwards arrow on top close vertical bar squared end fraction close parentheses times AC with rightwards arrow on top

*Menentukan vektor AB with bar on top pada AC with bar on top berdasarkan gambar diperoleh

AB with rightwards arrow on top equals open parentheses table row 4 row 0 end table close parentheses space dan space AC with rightwards arrow on top equals open parentheses table row 3 row 3 end table close parentheses

*Menentukan AB with rightwards arrow on top times AC with rightwards arrow on top

AB with rightwards arrow on top times AC with rightwards arrow on top equals open parentheses table row 4 row 0 end table close parentheses times open parentheses table row 3 row 3 end table close parentheses equals 4 times 3 plus 0 times 3 equals 12

*Menentukan open vertical bar AC with rightwards arrow on top close vertical bar

open vertical bar AC with rightwards arrow on top close vertical bar equals square root of 3 squared plus 3 squared end root equals square root of 9 plus 9 end root equals square root of 18 equals 3 square root of 2

*Menentukan proyeksi vektor AB with bar on top pada AC with bar on top.

table attributes columnalign right center left columnspacing 2px end attributes row cell Proyeksi space vektor end cell equals cell open parentheses fraction numerator AB with rightwards arrow on top times AC with rightwards arrow on top over denominator open vertical bar AC with rightwards arrow on top close vertical bar squared end fraction close parentheses times AC with rightwards arrow on top end cell row blank equals cell open parentheses 12 over open parentheses 3 square root of 2 close parentheses squared close parentheses times open parentheses table row 3 row 3 end table close parentheses end cell row blank equals cell open parentheses 12 over 18 close parentheses times open parentheses table row 3 row 3 end table close parentheses end cell row blank equals cell 2 over 3 times open parentheses table row 3 row 3 end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator 2 over denominator up diagonal strike 3 end fraction cross times up diagonal strike 3 end cell row cell fraction numerator 2 over denominator up diagonal strike 3 end fraction cross times up diagonal strike 3 end cell end table close parentheses end cell row cell Proyeksi space vektor end cell equals cell open parentheses table row 2 row 2 end table close parentheses end cell end table

Diperoleh proyeksi vektornya adalah open parentheses table row 2 row 2 end table close parentheses, berdasarkan gambar diperoleh bahwa AE with rightwards arrow on top equals open parentheses table row 2 row 2 end table close parentheses, sehingga proyeksi vektor AB with bar on top pada AC with bar on top adalah AE with bar on top.

Jadi, jawaban yang tepat adalah B.

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