= (x/r, y/r, z/r) r = be the unit radial vector, where x² + y? + z². Calculate the integral of 19. Let er F = e er over: a. the upper hemisphere of + y" +* = 9, outward-pointing normal. b. the octant 2 0, y 2 0, z 2 0 of the unit sphere centered at the origin.

Q: 2. Find T, N the unit bi-normal vector B, and k at the given t value. (2b) r(t) = ( cost, sint, In…

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Q: Let w = where z = ret®. 1) Show that by using Cauchy Riemann Equation (C.R. Eq.) in polar form that…

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Q: 25 mm 25 mm 100 mm 25 mm -75 mm-- -75 mm- 30 mm 100 mm 25 mm

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Q: Evaluate F. dS , where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 1, 0 < v<T…

A: since, y,-x,z3 and, ru,v=u cosv, u sinv,v So, F⇀ru,v=u cosv,-u sinv, v3 Now the normal upward vector…

Q: H=pz Csup ap te'sin dg tpan 2 At point (1, ,6)

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Q: Let A=[ Let B=A -t| 3. -2 where t is scalar, Fao which velve (s) of t is B singular?

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Q: find a unit normal vector to the surface at the indicated point

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

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Q: For the vector fleld G = (ye" + 3 cos(3r + y))i + (re + cos(3a + y)) j, tind the line integral of G…

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Q: Evaluate /| cos(x? + y²) dA, where D is the D disk x? + y <I Select one: a. -n O b. A O c. O O d. 2…

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

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Q: Let F = 3 x R, where is a constant vector. Calculate F. dR C on the line segment C connecting (1, 3,…

A: According to the given information, it is required to calculate the integral.

Q: Q1] Find a unit vector normal to the surface 3x2 у — узz? аt the point (1,-2, -1)

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

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Q: Let = In 2r, where r = √² + y². Express V as a multiple of the unit radial vector ê, = ( ) in R2…

A: We are given functionwhere

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

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Q: H=pz coup ap te'sing a4 tp'ar At point (1, ,0)

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Q: < 2x and –1 < u < 11. your solution using the form (*,*,*). Use symbolic notation and

A: Introduction: Surfaces in R3 have two degrees of freedom; it is possible to vary two parameters…

Q: Dz: tow ord the find the unit vector Curve y =x? at

A: Find the unit vector towards the curve y = x2 at x= 1: r→t=xti^+ytj^y=x2:Let xt=t  and…

Q: Compute the integral of ſA° · dľ°P2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector function…

A: We have to find the integral from point p1 TP p2.

Q: Evaluate /| F. d5 , where F = and S is the helicoid with - vector equation r(u, v) = 0 < u < 1, 0…

A: To evaluate the below vector surface integral. ∫∫SF⋅dS

Q: A force F acts on a particle that is moving in two dimensions along the semicircle x = 1 – cos 0, y…

A: Given the forces on a particle that is moving in 2D along the semicircle x=1-cosθ, y=sinθ, 0≤θ≤π.

Q: Identify the surface by eliminating the parameters from the vector-value r(u.v) = 3 cosv cosui +3…

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