Let S be the portion of the surface x + y“ + 2z“ = where y > x. Suppose S is oriented so that the unit normal vector at (0, 1,0) is (0, 1,0). Let F be a vector field satisfying V × F = (-2y², 2z², sin æ). Compute s(V × F) · ndS. Give your answer to 2 decimal places.

Q: Let S be the surface defined by the vector function R(u, v) = (2e" sin v, 2e" cos v, u²+u), where u…

A:

Q: Let y = Lal: Let L be the line spanned by u. and u %3D Write y as the sum of two orthogonal vectors,…

A:

Q: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

A:

Q: Find a vector-valued function r(t), that represents the following curve. Be sure to include an…

A: The vector valued functions in the parametric form can be represented as:…

Q: Let F(x, y, z) = xye" – 2° Ja and P(1,0, –1). Let S be the surface defined by the equation xye" –…

A:

Q: -y+25 Let F (x, y, z) := x+yz7 3+2⁹ let n be the outward unit normal vector. Evaluate Sf (curl F) ·…

A:

Q: The surface S is defined by x + y² + z³ = 3. Find a vector normal to S at the point A with position…

A: Given a surface S the normal vector to the surface at the point A is given by

Q: Find a unit normal vector of the surface at the given point P. x² + y² = 25, P: (4, 3,6)

A: The equation is x2+y2=25 and the point is P4, 3, 6. Now, the unit normal vector is n^=∇ϕ∇ϕ. Now, for…

Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: 33. Define T: R³ → R³ by y + 2z 2x +3y - z x +2y - 2z x - y a. Find all vectors in R' that are…

A:

Q: 1. Find the unit normal vector to the surface z = Vx2 + y? at the point (3, 4, 5).

A: A detailed solution is given below

Q: Let F = Jo Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (10,0,0),…

A:

Q: Let f(x,y, z) = a² + 2y² +z² and g(x,y,z)=z-xy. Find a unit vector u satisfying D.f (1.1,2)= 0 = D,…

A:

Q: A vector field is specified as G = 24xyax + 12(x² + 2)ay + 18z²az. Given two points, P(1, 2, - 1)…

A: Given: G=24xyax+12x2+2ay+18z2az P1,2,-1 Q-2,1,3 To find: c Unit vector directed from Q to P. d…

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: What is the principal unit normal vector for the curve: r(t) = (3t + 1)i + e'j .at the point P = (1,…

A: Let r(t) be the curve, then the unit tangent to the curve is given by T(t)= r'(t) / |r'(t)|. The…

Q: Let the temperature / in degrees at the point X,y,z), with distances measured in cm, be T(X,y,z)=5x…

A:

Q: Vector Field: F(x,y) = (xv, 3x, – 2y) and Surface: z = 4 - x - 3 y? Use the normal vector formula to…

A: Given surface z=4-x-3y2

Q: The normal vector to the tangent plane for the surface x²y³ z = 8, at the point (-1, 2, 1) is: 2 3…

A:

Q: Let S be the surface obtained by revolving the plane curve 2x=sqrt(9−y2) about the y-axis.Obtain a…

A: Given- Let S be the surface obtained by revolving the plane curve 2x = 9 - y2 about the y-axis. To…

Q: Let C be a curve defined by some vector function R with unit binormal B such that R(0) = (-2, 5, 4)…

A: Given C1 is a curve defined by some vector function R→ with unit binormal B→ such that R→(0)=-2,5,4,…

Q: Find a unit normal vector to the surface 6x2 + 2y2 + z2 = 225 at the point P : (5, 5, 5), and…

A:

Q: 8. Given the space curve C as the image of the vector valued function r(t) = 2ti+t³j+-t-¹ k OR r(t)…

A:

Q: 2. Let F(x, y) -yi-zj + zk be a vector field. Compute F FdS, where S is the hemisphere a² + y² +₂²…

A:

Q: 2. Find a unit normal vector to the surface x + y +2 = 5 at the point (0, 1, 2). Ans. Û + 2k)

A:

Q: Find a Vector ū: non zero Vector perpendicular to the

A:

Q: Write formulas for the unit normal and binormal vectors of a smooth space curve r(t)

A: The formulas for unit normal vector  and binomial vectors of a smooth space curve r(t).

Q: True or False: The vector (10, 2, –4) is normal to the surface x2 + y? – 22 = 22 at the point P =…

A:

Q: Find a vector normal to the surface x2 + yz = 5 at (2, 1, 1).

A: