Let F = (z, 0, y) and let S be the oriented surface parametrized by Þ(u, v) = (u² – v, u, v²) for 0 ≤ u ≤ 3, −1 ≤ v ≤ 4. (a) Calculate N and F. N as functions of u and v. (Use symbolic notation and fractions where needed.) N = (2v,-4uv,1) F.N= (b) Calculate the normal component of F to the surface at P = (6,3,9) = Þ(3, 3). (Use symbolic notation and fractions where needed.) normal component at P = Incorrect 2v³+u IF (c) Calculate F. ds. (Give your answer as a whole number.) F.dS= 63 1333 Incorrect

Q: 3. The point (1, k, 4) lies on the plane [x, y, z] = [1, 2, 0] + s[3, 0, 1] + t[2, −1, 1]. Find the…

A: Given point (1,k,4) is on plane.plane  is

Q: 1. Find the value of ø(0) for a solution ø(x) to the initial value problem: 6y" + y' – 2y = 0; y(1)…

A:

Q: Consider the set V of all vectors of the form (x y z)T where x, y and z are real numbers. 3. Show…

A:

Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the plane through U, V, and W, expressed in…

A:

Q: Let L be the line passing through the point P(−4, −3, 4) with direction vector d=[-3, 3, 0]T, and…

A:

Q: 1 -2 4 17. Let a 4 a2 -3 and b : For what 7 value(s) of h is b in the plane spanned by aj and a2?

A:

Q: Consider M = | 0 2 0 . Use the Cayley Hamilton theorem to find (M +4I)-1 where %3D 2 0 1 I is the 3…

A:

Q: Prove that the line x +1 = 글(-6) - lies in the plane 3x + y – 2 = 3.

A:

Q: 1. Let F(x, y,z) = (x + y², y + z²,z + x²). Let C be the triangle with vertices (1,0,0), (0,1,0),…

A: Consider the provided question,

Q: Find a vector function that represents the cur ve of intersection of the paraboloid z a + mnd the…

A: Given that, the paraboloid is z=x2+y2 and the cylinder is x2+y2=22. The projection of the of the…

Q: B) Find the value of k so that the line: [x, y, z) = [2, -2, 0] + [3, 5, k] is parallel to the…

A: As per guidelines of Bartleby i am supposed to solve on first part , if you want more solution then…

Q: Find the distance from y to the plane in R spanned by the set {u1, uz} 4 - 3 -3 y = -9 -4 Uz 2 4 1…

A: Solution   Given,       Find the distance from  γ to the plane  in R3       spanned  by the  set…

Q: Use Stoke's Theorem to evaluate $. F · dR, where F (x, y, z) = (z²,xy, xz) and C is the triangle in…

A:

Q: Consider the following function. T: R² - R?, T(X, V) = (Vã, sxy, Vỹ) Find the following images for…

A:

Q: Let u = 4 h = V= and w= 1 . For what value of h is w in the plane spanned by u am

A:

Q: Let = xi + yj + zk be the position vector to any point P(x,y,z) on a surface $(x, y,z)=c. a) Write…

A: According to question,Given Position vector at Point Px, y, z,r→ = x i^ + y j^ + z k^,ϕx, y, z = c

Q: Given is the plane V : a · x = 9 with a = (2, -3,6)t. Calculate the distance from O= (0,0,0) and…

A: Given that:The Plane  with To find: The distance from  and  to V.Concept:The distance d between a…

Q: Find a parametric representation for the surface. the plane that passes through the point (0, -1, 5)…

A:

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

A: Given Information -  The distance from the point R = (c,1,-1) to the plane x+y-z = 2 is 2. We have…

Q: Find a parametric representation for the surface. the plane that passes through the point (0, -1, 2)…

A: Given that: The plane passes through (0,-1,2) and contains a vector 4,1,5,-3,4,2. The parametric…

Q: Find the distance from y to the plane in R³ spanned by the set (U₁, U₂} 6 - 2 4 y = -9 a. b. C. 43₁…

A:

Q: Which of these is the correct parametrization of the line connecting (1,2,5) and (0,3,– 1)? A. x =…

A: We know that parametrization of the line connecting pointsx1,y1,z1,x2,y2,z2 is given by x=x1+tx2-x1;…