Roboguru

Diketahui vektor dan Proyeksi vektor orthogonal pada adalah....

Diketahui vektor u with rightwards arrow on top equals open parentheses table row 0 row 2 row 2 end table close parentheses dan v with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 0 row 2 end table close parentheses. Proyeksi vektor orthogonal u with rightwards arrow on top pada v with rightwards arrow on top adalah....

  1. -i + k

  2. negative i plus 1 half k

  3. -i - k

  4. -2i + k

  5. 2i - k

Jawaban:

Proyeksi space vektor space orthogonal space straight u with rightwards arrow on top space pada space straight v with rightwards arrow on top space adalah space  fraction numerator straight u with rightwards arrow on top. straight v with rightwards arrow on top over denominator open vertical bar straight v with rightwards arrow on top close vertical bar squared end fraction. straight v with rightwards arrow on top  Jadi comma space proyeksi space orthogonal space vektor space straight a with rightwards arrow on top equals open parentheses table row 0 row 2 row 2 end table close parentheses space pada space vektor space straight b with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 0 row 2 end table close parentheses  fraction numerator straight a with rightwards arrow on top. straight b with rightwards arrow on top over denominator open vertical bar straight b with rightwards arrow on top close vertical bar squared end fraction. straight b with rightwards arrow on top  equals fraction numerator open parentheses table row 0 row 2 row 2 end table close parentheses. straight space open parentheses table row cell negative 2 end cell row 0 row 2 end table close parentheses over denominator open parentheses square root of left parenthesis negative 2 right parenthesis squared plus 0 squared plus open parentheses 2 close parentheses squared end root close parentheses squared end fraction. open parentheses table row cell negative 2 end cell row 0 row 2 end table close parentheses  equals 4 over 8. open parentheses table row cell negative 2 end cell row 0 row 2 end table close parentheses  equals 1 half. open parentheses table row cell negative 2 end cell row 0 row 2 end table close parentheses  equals 1 half open parentheses negative 2 straight i with rightwards arrow on top plus 2 straight k with rightwards arrow on top close parentheses  equals negative straight i with rightwards arrow on top plus straight k with rightwards arrow on top

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