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Diketahui vektor dan Proyeksi vektor orthogonal te...

Diketahui vektor p with rightwards arrow on top equals 11 i plus 4 j plus 3 k dan q with rightwards arrow on top equals 2 i plus 5 j plus 11 k. Proyeksi vektor orthogonal p with rightwards arrow on top terhadap q with rightwards arrow on top adalah....

  1. 2i - 5j - 11k

  2. negative i minus 5 over 2 j minus 11 over 2 k

  3. i plus 5 over 2 j plus 11 over 2 k

  4. negative i plus 5 over 2 j plus 11 over 2 k

  5. - i - 5j - 11k

Jawaban:

Proyeksi space vektor space orthogonal space straight p with rightwards arrow on top space dan space straight q with rightwards arrow on top space adalah space fraction numerator straight p with rightwards arrow on top. straight q with rightwards arrow on top over denominator open vertical bar straight q with rightwards arrow on top close vertical bar squared end fraction straight q with rightwards arrow on top  Jadi comma space proyeksi space orthogonal space vektor space straight p with rightwards arrow on top equals open parentheses table row 11 row 4 row 3 end table close parentheses space pada space vektor space straight q with rightwards arrow on top equals open parentheses table row 2 row 5 row 11 end table close parentheses  fraction numerator open parentheses table row 11 row 4 row 3 end table close parentheses. open parentheses table row 2 row 5 row 11 end table close parentheses over denominator open parentheses square root of 2 squared plus 5 squared plus 11 squared end root close parentheses squared end fraction open parentheses table row 2 row 5 row 11 end table close parentheses equals fraction numerator 22 plus 20 plus 33 over denominator open parentheses square root of 150 close parentheses squared end fraction open parentheses table row 2 row 5 row 11 end table close parentheses equals 75 over 150 open parentheses table row 2 row 5 row 11 end table close parentheses equals 1 half open parentheses table row 2 row 5 row 11 end table close parentheses equals straight i plus 5 over 2 straight j plus 11 over 2 straight k

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