5. Suppose that we have a function f(x, y) and a point P = (a, b) in the domain where ) and = 0. Then the tangent plane Tpf at P is parallel to what well-known = 0 plane? Prove your claim (a picture is not sufficient... recall how we define two planes being parallel algebraically in terms of some important vectors in order to write a good proof).

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Q: 19. Suppose that the normal unit vector N of a surface S at z =f (x,y) is determined, how does the…

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Q: Let z E C. Draw the following regions on the xy-plane. Justify your work. (a) {z E C : 4 < |z| < 6}…

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Q: 6) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 4.1., # 20) Show that, at…

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Q: Let R = (c, 1,-1) where c denotes a real number. Let ä denote the plane x + y – z = 2. Find the…

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Q: 12) Find the intersection of the plane: x – z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

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Q: 9. Find the equation of the plane through P(1,1,4) that is parallel to the plane x+ 5y – z + 8 = 0

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Q: Find the equations of the tanget plane and normal line to the graph of In(2?)x-을=3y3-VE at the point…

A: Equation of tangent plane f(x, y, z) = k at x0, y0, z0 is, fxx0, y0, z0x-x0+fyx0, y0, z0y-y0+fzx0,…

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Q: 19. Suppose that the normal unit vector N of a surface S at z = f(x, y) is determined, how does the…

A: Note: As company policy, we solve first question only. Please resubmit the rest of the questions in…

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Q: 4. (a) Find the mid-point, unit tangent vector and unit normal vector at the mid-point of a planar…

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Q: Show that the curve a(t) = (t, , ) lies in a plane and find the equation of this plane.

A: For all 't' , we have α'(t) = 1 , -1t2 ,-1 - 1t2α"(t) = 0 , 2t3 , 2t3 Now  α'(t) × α"(t) = 2t3 ,…

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Q: 4. If ricost cosh t+j sint sinh t, where i and j are constant orthogonal vectors prove that (a)…

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Q: Q2:Prove that the line (x-1)/2=(y+1)/3=(z-2)/(4 ) is parallel to the plane x-2y+z=6 ?

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Q: Are the planes given by Π1 : 2x − 3y + z − 1 = 0 and Π2 : 3x − 2y + 4z − 7 = 0 parallel? Justify…

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Q: 14. Given F(1) = (-1,3,0) F'(1) = (2,–2, 1) F"(1) = (0,–1, 4), What %3D is the vector equation of…

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Q: Let vector Ñ be normal to plane x – 5y – 2z = 3, and let Ē = (3, – 2, 1). Find the following. 1. The…

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