Formulas Calc III - Calculus III Formulas u v cos = uv(u v...

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Calculus III Formulas v u v u = θ cos ( 29 v v v u u proj v = 2 W= Q P F proj Q P W= Q P F A= θ sin v u v u = × 3 2 1 3 2 1 3 2 1 ) ( w w w v v v u u u w v u = × V= ) ( w v u × 2 1 2 1 cos n n n n = θ D= n n Q P Q P proj n = D= u u Q P × x y y x r z z r y r x = + = = = = θ θ θ tan sin cos 2 2 2 + + = = + + = = = = 2 2 2 2 2 2 2 arccos tan cos sin sin cos sin z y x z x y z y x z y x φ θ ρ φ ρ θ φ ρ θ φ ρ + = + = = = = 2 2 2 2 2 2 2 arccos cos sin z r z z r z r φ ρ φ ρ θ θ φ ρ , ) ( ' ) ( ' ) ( t r t r t T = N( t) = ) ( ' ) ( ' t T t T [ ] v a v T a v t D T a = = = 2 2 ' T a a v a v N a T v N a - = × = = = [ ] [ ] [ ] dt t r dt t z t y t x s b a b a = + + = ) ( ' ) ( ' ) ( ' ) ( ' 2 2 2 K= 3 ) ( ' ) ( ' ' ) ( ' ) ( ' ) ( ' t r t r t r t r t T × = K= [ ] 2 3 2 ) ' ( 1 ' ' y y + = 2 ) ( ) ( ) ( t v t
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