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MIA 2 - Vector Concept Review.pdf

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MIA 2 - Vector Concept Review.pdf

  1. 1. CONCEPT REVIEW VECTOR vs SCALAR Berupa nilai dengan arah tertentu Berupa nilai/besaran Τ¦ π‘Ž = π‘š ΖΈ 𝑖 + 𝑛 ΖΈ 𝑗 + 𝑝෠ π‘˜ π‘Ž = π‘₯, βˆ€π‘₯ ∈ ℝ Hasil dari operasi hitung 2 vektor: Τ¦ π‘Ž + 𝑏, Τ¦ π‘Ž βˆ’ 𝑏, Τ¦ π‘Ž Γ— 𝑏 Hasil dari perkalian skalar vektor (vector dot product) Τ¦ π‘Ž βˆ™ 𝑏 Hasil dari menghitung Panjang vektor Τ¦ π‘Ž , Τ¦ π‘Ž + 𝑏 , Τ¦ π‘Ž βˆ’ 𝑏 , Τ¦ π‘Ž Γ— 𝑏 , Τ¦ π‘Ž βˆ™ 𝑏 dll
  2. 2. CONCEPT REVIEW PENULISAN VEKTOR Τ¦ π‘Ž = ΰ΄€ π‘Ž = ො π‘Ž = 𝒂 OPERASI MATRIKS Τ¦ 𝑔 = π‘₯ 𝑦 𝑧 Τ¦ 𝑔𝑇 = π‘₯ 𝑦 𝑧 β„Ž = 1 2 3 4 5 6 β„Žπ‘‡ = 1 3 5 2 4 6 Misalkan Τ¦ 𝑧 = π‘Ž 𝑏 𝑐 𝑑 𝑒 𝑓 𝑔 β„Ž 𝑖 𝐷𝑒𝑑 Τ¦ 𝑧 = π‘Ž 𝑏 𝑐 𝑑 𝑒 𝑓 𝑔 β„Ž 𝑖 𝐷𝑒𝑑 Τ¦ 𝑓 = π‘Ž. 𝑒. 𝑖 + 𝑏. 𝑓. 𝑔 + 𝑐. 𝑑. β„Ž βˆ’ [ 𝑔. 𝑒. 𝑐 + β„Ž. 𝑓. π‘Ž + (𝑖. 𝑑. 𝑏)] Τ¦ π‘Ž = (π‘š, 𝑛, 𝑝) 𝑏 = (𝑐, 𝑑, 𝑓) Τ¦ π‘Ž = π‘š 𝑛 𝑝 𝑏 = 𝑑 𝑒 𝑓 Misalkan: Τ¦ π‘Ž = π‘šΤ¦ 𝑖 + 𝑛Ԧ 𝑗 + π‘π‘˜ 𝑏 = 𝑑Ԧ 𝑖 + 𝑒Ԧ 𝑗 + π‘“π‘˜
  3. 3. CONCEPT REVIEW Τ¦ π‘Ž + 𝑏 2 = Τ¦ π‘Ž 2 + 𝑏 2 + 2 Τ¦ π‘Ž 𝑏 cos πœƒ Τ¦ π‘Ž + 𝑏 2 = Τ¦ π‘Ž 2 + 𝑏 2 + 2 Τ¦ π‘Ž β‹… 𝑏 Τ¦ π‘Ž βˆ’ 𝑏 2 = Τ¦ π‘Ž 2 + 𝑏 2 βˆ’ 2 Τ¦ π‘Ž 𝑏 cos πœƒ Τ¦ π‘Ž + 𝑏 2 = Τ¦ π‘Ž 2 + 𝑏 2 βˆ’ 2 Τ¦ π‘Ž β‹… 𝑏
  4. 4. CONCEPT REVIEW
  5. 5. CONCEPT REVIEW
  6. 6. π’š = 𝐬𝐒𝐧 𝒙 π’š = 𝐜𝐨𝐬 𝒙

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