Calculus_final_formulasheet

# Calculus_final_formulasheet - 12.1 Eq of Sphere x a 2 Mid...

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12.1 Eq. of Sphere: 2 2 2 2 ( ) ( ) ( ) x a y b z c r - + - + - = Mid. Pt: 1 2 1 2 1 2 , , 2 2 2 x x y y z z + + + 12.3 Norm: 2 2 2 ( , , ) a a b c a a b c = + + = Unit Vector: a a U a = 12.4 0 cos( ) a b a b a b a b θ = = g g ( ) b b b b b comp a a U proj a a U U = = g g 12.5 Volume of Parallelopiped: ( ) a b c a g Area of Parallelogram: a b a 0 a b a b a = P Cross product give u vector to the plane ab. 12.6 Vector Parametric: 0 ( ) r t r td = + r ur Scalar Parametric: 0 1 0 2 0 3 ( ) ( ) ( ) x t x td y t y td z t z td = + = + = + Symmetric: 0 0 0 1 2 3 x x y y z z d d d - - - = = 12.7 Unit Normal: N N U N = uur Angle btw 2 planes: 1 2 cos( ) N N U U = g ( , , ) N A B C = uur Eq. of a plane: 0 0 0 ( ) ( ) ( ) 0 A x x B y y C z z - + - + - = Distance from pt. 1 P to plane 0 P : 1 0 2 2 2 ( , ) Ax By Cz D d P P A B C + + + = + + Distance from pt. 1 P to line L 0 1 1 ( , ) P P d d P L d a = uuuur 13.3 Unit Tangent Vector: ( ) ( ) ( ) r t T t r t a = ( ) ( ) ( ) T t N t T t a = Principal Normal Vector. 13.4 Arc Length

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Calculus_final_formulasheet - 12.1 Eq of Sphere x a 2 Mid...

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