Let S be the parabolic arch given by r(u,v) = (u+v, u-v, 4-u²) where (u, v) € [−2, 2] × [0, 1].Compute the normal vector xrHere is a picture of this surface. Draw (in several representative places) the directionof the normal vectors that you computed in the previous part of the problem.Setupand evaluate the flux integral of F = j across S.I

Step 1: Step 2: Step 3: Step 4:

Answered: Let S be the parabolic arch given by…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 10E

See similar textbooks

Similar questions

Find a vector n normal to the plane with the equation 6z – (5x + 5y) = −1. n = (-5, >
Find a vector normal to the surface 3z 3 + x 2 y - y 2 x = 1 at P =(1,-1,1) .
Please recheck and provide clear and complete step-by-step solution in scanned handwriting or computerized output thank you
Let S be the parabolic arch given by r(u, v) = (u+v, u−v, 4-u²) where (u, v) € [−2, 2]×[0, 1]. Compute the normal vector × ди Iv' Ər Here is a picture of this surface. Draw (in several representative places) the direction of the normal vectors that you computed in the previous part of the problem. Set up and evaluate the flux integral of F = xj across S.
−Y+z5 Let F (x, y, z) := x+yz7 3+2⁹ let ŉ be the outward unit normal vector. Evaluate ſf (curl F) · ndS. (Use syntax like 2*pi/3 .) Let S be the upper half of the sphere of radius 2 centered at the origin. At each point of S
Find equations of the tangent plane and normal line to the surface x=6y^2+5z^2−459 at the point (2, 6, 7).Equation of the tangent plane (make the coefficient of x equal to 1): =0.Vector equation of the normal line: l(t)=⟨2,, ⟩+t⟨1, , ⟩.HINT. Represent the given surface as a level surface of a certain function f(x,y,z), that is, re-write the equation of the surface in the form �(�,�,�)=c, where �(�,�,�) is a function of 3 variables and f is a constant. Then find the gradient vector of the function f at the given point. The tangent plane to the surface at that point is orthogonal to the gradient vector, and the normal line -- parallel to it. This allows us to write the equations of both tangent plane and normal line.
Find a vector function that represents the curve of intersection of the two surfaces. The cone y = V = v 2x2 +9z2 and the plane y = 5+3z r(t) = ( 1 t2 2' 15 6. 1 r(t) = (t, 1 t2 2' 15 6. 1 5 r(t) = (! + 구 t, 15 %3D 6. r(t) = (t, - + 2' 15 6. r(t)%3D = ( t, ť + 15 6.
Let S be the parabolic arch given by r(u, v) = (u+v, u−v, 4−u^2) where (u, v) ∈ [−2, 2]×[0, 1]. Compute the normal vector ∂r/∂u × ∂r/∂v . Here is a picture of this surface. Draw (in several representative places) the directionof the normal vectors that you computed in the previous part of the problem. Set up and evaluate the flux integral of F = x j across S.
Find a vector normal to the surface x2 + yz = 5 at (2, 1, 1).
Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 – cos (v)) sin (u), z = sin (v) at the image of a point (u, v) for –x < v < a and -a < u < a. (Write your solution using the form (*,*,*). Use symbolic notation and fractions where needed.) no = Identify this surface. ellipsoid hyperboloid torus cylinder
What is the principal unit normal vector for the curve: r(t) = (3t + 1)i + e'j .at the point P = (1,1)? 3i – j V10 Ob. 3i +j V10 Oc. V10 3/10 i+ 10 10 od There is no unit normal vector for this curve at this point. V10 3V10 -j 10 10
Which of the vector functions below represents the curve of intersection of the following two surfaces: x² +4y²+4z² = 16 and y = x². Select one: ○ a. r (t) = (t, t², O b. r (t) = (t, t², |○ c. r (t) = (t, t₁, ○ d. r (t) = t, -t² = (t, 16++²-4+4 4 1 16-12-4t 4 O e. None of the above ○ f. r (t) = (t, t², √ 16-12+4t 4 16-12-4t 4 4-12-4t4 4

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS