math_27

Transcript

1. 27 ϕΫτϧͷ಺ੵͱΣͷؔ܎ ౷ܭֶ͕࠷ڧͷֶ໰Ͱ͋Δɹ਺ֶฤ
2. લճͷτϐοΫ ϕΫτϧΛ࢖͏͜ͱͰߴີ౓ʹσʔλΛද͢͜ͱ͕Ͱ͖Δ
3. ࠓճͷτϐοΫ • ϕΫτϧͷ಺ੵ(υοτੵ) • ಺ੵܭࢉͷϧʔϧ • ಺ੵΛγάϚͰද͢
4. ϕΫτϧͷ಺ੵ a ⋅ b = ∥a∥∥b∥ cos θ a = (a1 a2 ⋯ an ) b = (b1 b2 ⋯ bn ) BͱCͷͳ֯͢Вʹ͓͍ͯ ∥a∥ = a2 1 + a2 2 + ⋯ + a2 n ·ͨɺϕΫτϧͷେ͖͞ΛϕΫτϧͷϊϧϜͱ΋ݴ͍ɺ࣍ࣜͰද͢
5. ಺ੵΛزԿతʹݟΔ (P.274 ਤ4-5) ͓ޓ͍ͷ޲͖Λἧ͑ͯɺֻ͚ͨ΋ͷ
6. ಺ੵܭࢉͷϧʔϧ |a| |b| cosθ͸ͦΕͧΕεΧϥʔͳͷͰɺP.26ͷܭࢉ๏ଇ͕੒Γཱͭ ⭕ ަ׵๏ଇ ⭕ ෼഑๏ଇ ⚠ ݁߹๏ଇ ಺ੵ͸̎ͭͷϕΫτϧͷͳ֯͢ͳͷͰɺpa=cͰͳ͍ͱ❌ ⃗ a ⃗ b = ⃗ b ⃗ a (p ⃗ a ) ⋅ ⃗ b = p( ⃗ a ⋅ ⃗ b ) = ⃗ a ⋅ (p ⃗ b ) ⃗ a ⋅ ( ⃗ b + ⃗ c ) = ⃗ a ⋅ ⃗ b + ⃗ a ⋅ ⃗ c ⃗ a ⋅ ( ⃗ b + ⃗ c ) ≠ ( ⃗ a ⋅ ⃗ b ) ⋅ ⃗ c
7. ಺ੵΛγάϚͰද͢ a = (a1 a2 ⋯ an ) b = (b1 b2 ⋯ bn ) BͱCͷͳ֯͢Вʹ͓͍ͯ a ⋅ b = ∥a∥∥b∥ cos θ ɹɹ = n ∑ i=1 ai bi ٯʹɺʮγάϚͷ୅ΘΓʹϕΫτϧΛ࢖ͬͯγϯϓϧͳදه͕Ͱ͖ Δɻʯͱ΋ݴ͑Δɻ
8. ·ͱΊ γάϚͷ୅ΘΓʹϕΫτϧΛ࢖ͬͯγϯϓϧͳදه͕Ͱ͖Δɻ
9. ͓·͚ • ֎ੵ(Ϋϩεੵ) ͨͩ͠ɺO࣍ݩϕΫτϧʹରͯ͠ɺ֎ੵͷఆٛ͸ͳ͍ a ⋅ b = ∥a∥∥b∥ sin θ