Roboguru

Diketahui space a with rightwards harpoon with barb upwards on top equals 2 i plus 2 j plus 9 k space dan space b with rightwards harpoon with barb upwards on top equals 2 i minus 2 j plus k. space Proyeksi space vektor space orthogonal space a with rightwards harpoon with barb upwards on top space pada space b with rightwards harpoon with barb upwards on top  adalah space....

  1. 3i-3j+k

  2. 3i-5j-2k

  3. 4i-4j+2k

  4. 2i-2j+k

  5. 5i+5j+5k

Jawaban:

Proyeksi space vektor space orthogonal space a with rightwards harpoon with barb upwards on top space pada space b with rightwards harpoon with barb upwards on top space adalah space fraction numerator a with rightwards harpoon with barb upwards on top. b with rightwards harpoon with barb upwards on top over denominator open vertical bar b with rightwards harpoon with barb upwards on top close vertical bar squared end fraction b with rightwards harpoon with barb upwards on top  Jadi comma space proyeksi space orthogonal space vektor space a with rightwards harpoon with barb upwards on top equals open parentheses table row 2 row 2 row 9 end table close parentheses space pada space vektor space b with rightwards harpoon with barb upwards on top equals open parentheses table row 2 row cell negative 2 end cell row 1 end table close parentheses  fraction numerator open parentheses table row 2 row 2 row 9 end table close parentheses open parentheses table row 2 row cell negative 2 end cell row 1 end table close parentheses over denominator left parenthesis square root of 2 squared plus left parenthesis negative 2 right parenthesis squared plus 1 squared end root right parenthesis squared end fraction open parentheses table row 2 row cell negative 2 end cell row 1 end table close parentheses equals fraction numerator 4 minus 4 plus 9 over denominator left parenthesis square root of 9 right parenthesis squared end fraction open parentheses table row 2 row cell negative 2 end cell row 1 end table close parentheses equals open parentheses table row 2 row cell negative 2 end cell row 1 end table close parentheses equals 2 i with rightwards harpoon with barb upwards on top minus 2 j with rightwards harpoon with barb upwards on top plus k with rightwards harpoon with barb upwards on top

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