a surface is defined by the parametric form. S(u,v)= X(u,v)i + Y(u,v)j + Z(u,v)k, where 0<= u <=2pi and 0<= v <=1 X(u,v) = (v2+1)cos2u Y(u,v) =vsinu Z(u,v) =-(v2+1) a. determine the normal vector of the surface S b. determine the unit normal vector of S(0,1/2) that point onward

Q: Match each parametrization with the corresponding surface. (i) (ii) (iii) (iv) (v) Answer Bank (u,…

A:

Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

A:

Q: If Φ = xy^2 + 6 z^3 x^2, find  ∇Φ and |∇Φ| at the point (6,2,2)​ ​

A:

Q: Use Green's Theorem to find the work done by F(x,y)=x(3x+y)i+xy^2j in moving a particle from the…

A:

Q: (a) Find a vector parametric equation for the ellipse that lies on the plane x + 3y + z = 5 and…

A:

Q: Determine an equation for the plane that's tangent to the surface z = 6x2 + 7y2 at point (-3, -2,…

A:

Q: Find an equation of the plane that contains point A(5,1,1) and the line that is given with…

A: Please see the below picture for detailed solution.

Q: Find a set of parametric equations for the graph of y = 4x² + 2 using the parameter t = x – 3 O x =…

A: Given parameter- t=x-3 Then,  x=t+3

Q: Consider the curve r(t) = (a) Pick any three points along the curve. Then find an equation of the…

A: