Consider the surface S with surface parameterisation r(u, v) = 3u sin(v) i + 4u sin(v)j + vk for 0 ≤u≤ 1 and 0 ≤ v ≤ π. Ər ər (1) Calculate the tangent vectors, and to the surface S. du əv' (2) Use your results in part 1 to find a normal vector N to the surface S. (3) Find the length of the normal vector to the surface S. (4) Use the result in part 3 (and the surface parameterisation) to find the surface area of S. Start by writing the general mathematical expression for finding the surface area of a surface.

Q: .4 || (cos²e + sin?e) dp dz de 8 2(0*cos?8 + p*sin?e) p dp dz de

A:

Q: IDENTIFY FROM THE THE SURFACE BY EUMINATING THE PARAMETERS VECTOR VALUED Function 3 COS v Cos ui + 3…

A:

Q: Calculate the vectors A and C curves given below with aA dl

A: In this question, we have to calculate the line integral in both parts.

Q: Check that the point (-2, 2, 4) lies on the surface cos(x + y) = exz+8 (a) View this surface as a…

A:

Q: At point (6, 3, 162), find the parametric equations for the normal line to the surface z = 5x^2 -…

A:

Q: Find equations for the tangent plane and the normal line at point Po(1,1,0) on the surface - 6 cos…

A: The given surface is -6cos (πx) +6x2y +2exz+6yz=14 Equation of the tangent plane to the surface is…

Q: 36 for 0 <= u <= 6 and 0 <= v <= 2(pi) where <= is less then equal too where pi = 3.1415

A: Introduction: An ellipse is the locus of all points that satisfy the equations.x = a sint,  y = b…

Q: Find the lines curvatures, the first and second fundamental forms of the surface: the surface

A: As per the question we are given a surface. And we have to find its first and second fundamental…

Q: Determine the following: (a) the general equation of the tangent plane to the surface at Po (b) the…

A:

Q: The unit tangent I already found which was correct was (32 , 24t , 9t^2 )*1/41 I need the…

A: To find unit normal vector

Q: t-) For each surface below, find the normal vector and equation of the tangent plane at the given…

A: Use definition of tangent plane and norman vector.  According to guidelins, we solve only first 3…

Q: Consider the surface S of equation 2 = x² + y*" An equation for the tangent line tangent to S at…

A:

Q: Part B please g(x,y,z)=x^2+y^2+(z-3)^2

A:

Q: What is the relationship between the curvature of a surface and its Gaussian curvature in the…

A: Differential Geometry is the branch of mathematics that uses the methods of calculus and linear…

Q: b\ Find the domain of the functions: (1) y = (2) y = = (3)f(x) =

A:

Q: A particle travels along the curve r(t) = (cos t, sin t, In(cos t)). a) Find the distance the…

A:

Q: Find the parametric equations of normal line to the surface given by f(x, y) = tan v x2 +y2 at the…

A:

Q: This surface (dreamed up by Steiner while in Rome) looks smooth but is non-orientable, with the…

A: Given: The parametrization for the surface is given by σ(u,v)=x,y,z=sin2usinv,sin2ucosv,cos2usin2v…