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Pertanyaan

Diketahui ∣ ∣ ​ u ∣ ∣ ​ = 12 , ∣ ∣ ​ v ∣ ∣ ​ = 4 , dan sudut antara vektor u dan v adalah 3 2 π ​ . Proyeksi vektor u pada v adalah ....

Diketahui , dan sudut antara vektor  dan  adalah . Proyeksi vektor  pada  adalah .... 

  1. 3 over 2 straight v with rightwards arrow on top

  2. 2 over 3 straight v with rightwards arrow on top

  3. 1 half straight v with rightwards arrow on top

  4. negative 1 half straight v with rightwards arrow on top

  5. negative 3 over 2 straight v with rightwards arrow on top

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N. Nisa

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

jawaban yang tepat adalah E.

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Pembahasan

Pembahasan
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Pertama-tama, tentukan perkalianvektor pada . maka, proyeksi vektor pada . Jadi, jawaban yang tepat adalah E.

Pertama-tama, tentukan perkalian vektor  straight u with rightwards arrow on top pada straight v with rightwards arrow on top.

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell fraction numerator straight u with rightwards arrow on top times straight v with rightwards arrow on top over denominator open vertical bar straight u with rightwards arrow on top close vertical bar times open vertical bar straight v with rightwards arrow on top close vertical bar end fraction end cell row cell open vertical bar straight u with rightwards arrow on top close vertical bar times open vertical bar straight v with rightwards arrow on top close vertical bar times cos space alpha end cell equals cell straight u with rightwards arrow on top times straight v with rightwards arrow on top end cell row cell straight u with rightwards arrow on top times straight v with rightwards arrow on top end cell equals cell open vertical bar straight u with rightwards arrow on top close vertical bar times open vertical bar straight v with rightwards arrow on top close vertical bar times cos space fraction numerator 2 straight pi over denominator 3 end fraction end cell row blank equals cell 12 times 4 times cos space 120 degree end cell row blank equals cell 48 times open parentheses negative 1 half close parentheses end cell row blank equals cell negative 24 end cell end table

maka, proyeksi vektor  straight u with rightwards arrow on top pada straight v with rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row cell straight c with rightwards arrow on top end cell equals cell fraction numerator straight u with rightwards arrow on top times 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 times straight v with rightwards arrow on top end cell row blank equals cell fraction numerator negative 24 over denominator 4 squared end fraction straight v with rightwards arrow on top end cell row blank equals cell negative 3 over 2 straight v with rightwards arrow on top end cell end table 

Jadi, jawaban yang tepat adalah E.

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Diketahui vektor a = ⎝ ⎛ ​ − 1 − 3 2 ​ ⎠ ⎞ ​ dan b = ⎝ ⎛ ​ − 2 6 1 ​ ⎠ ⎞ ​ . Vektor proyeksi ortogonal dari vektor b pada vektor a adalah ....

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