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math_27
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Utree
May 08, 2019
Education
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39
math_27
Utree
May 08, 2019
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Transcript
27 ϕΫτϧͷੵͱΣͷؔ ౷ܭֶ͕࠷ڧͷֶͰ͋Δɹֶฤ
લճͷτϐοΫ ϕΫτϧΛ͏͜ͱͰߴີʹσʔλΛද͢͜ͱ͕Ͱ͖Δ
ࠓճͷτϐοΫ • ϕΫτϧͷੵ(υοτੵ) • ੵܭࢉͷϧʔϧ • ੵΛγάϚͰද͢
ϕΫτϧͷੵ a ⋅ b = ∥a∥∥b∥ cos θ a =
(a1 a2 ⋯ an ) b = (b1 b2 ⋯ bn ) BͱCͷͳ֯͢Вʹ͓͍ͯ ∥a∥ = a2 1 + a2 2 + ⋯ + a2 n ·ͨɺϕΫτϧͷେ͖͞ΛϕΫτϧͷϊϧϜͱݴ͍ɺ࣍ࣜͰද͢
ੵΛزԿతʹݟΔ (P.274 ਤ4-5) ͓ޓ͍ͷ͖Λἧ͑ͯɺֻ͚ͨͷ
ੵܭࢉͷϧʔϧ |a| |b| cosθͦΕͧΕεΧϥʔͳͷͰɺP.26ͷܭࢉ๏ଇ͕Γཱͭ ⭕ ަ๏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
ੵΛγάϚͰද͢ a = (a1 a2 ⋯ an ) b =
(b1 b2 ⋯ bn ) BͱCͷͳ֯͢Вʹ͓͍ͯ a ⋅ b = ∥a∥∥b∥ cos θ ɹɹ = n ∑ i=1 ai bi ٯʹɺʮγάϚͷΘΓʹϕΫτϧΛͬͯγϯϓϧͳදه͕Ͱ͖ Δɻʯͱݴ͑Δɻ
·ͱΊ γάϚͷΘΓʹϕΫτϧΛͬͯγϯϓϧͳදه͕Ͱ͖Δɻ
͓·͚ • ֎ੵ(Ϋϩεੵ) ͨͩ͠ɺO࣍ݩϕΫτϧʹରͯ͠ɺ֎ੵͷఆٛͳ͍ a ⋅ b = ∥a∥∥b∥ sin
θ