7. Consider the Surface S:z = 52² + 5y?. An equation of the plane tangent to Sat the point P (3, 3, 90) is given by A) 30x + 30y – z = 90 в) — 15г — 15у +39 С) —30х — 30у — г 3 180 D) 30x + 30y +z = 90

Q: What is the equation of the plane to the surface z = e3y sin(3x) +2 at the point P ,0, 3 %3D O x- y…

A: The solution is given in the next step.

Q: Suppose we have a quadric surface described by 1 (r, y, z) | 1 1 = 7. 1 -4 Using canonical…

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Q: Evaluate ff.dS, where (a) v = (xy, -x², x +z) and S is the part of the plane 2x + 2y + z = 6…

A: Problem is solved using concept of double integral.

Q: Calculate , z² dS if S is the prism whose base is the triangle in the limited xy plane by the x axis…

A: Here given figure is Since prism has 5 surfaces (1)-OAB (2) OADE (3) CDE (4) OBCD (5) ABCE

Q: 1. 3 Consider the parametric surface 7(u, v) = (2uv, u? - v, u² +v²), where u +v < 2. Evaluate the…

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Q: Let D be the solid in space lying beneath the ry-plane and between the sphere r2 + y? + z² = 3 and…

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Q: Evaluate f, A.n ds, where A = zi +j- 3y²zk and S is the surface of cylinder x? + y? = 16 included in…

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Q: Use Divergence Theorem to evaluate ,0i +rj +ryh) ds, Q#3(a) where S is the upper part of the sphere…

A: As per bartleby instruction when more then one question is given only one has to be answered. Please…

Q: Show by Vector mothads that th ditonce hom fhe fornt P.(Xx, Y,, Z) to the plane Ax -+By+cz-D26 t of…

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Q: A point moves along the intersection of the elliptic paraboloid z = 9x? + 3y² and the plane.x…

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Q: Let S be the closed surface composed of the parabaloid z = x2 + y? and the planes z = 2 and z = 4.…

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Q: Let C be the curve of intersection of the parabolic cylinder x² = 2y, and the surface 3z = xy. Find…

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Q: Given F(x, y, z) = -yzi + xzj – xyzk be a vector function that passes through a surface S of z + x2…

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Q: 3, Consider Hhe following twe suctaces 2=2xy Sur 82- 5y-82=-13 a) Show that the surdaces inter sect…

A: Let the bequation of surface is given by F(x,y,z)=0 and if f is differentiable at point…

Q: 8. Let S be the surface {(x, y, 2) | a = y? + 22 + 1}. Find every point (ro, yo, zo) on S so that…

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Q: Evaluate ſ F . n dS if F = (x + y² ™)ī − (2x)j + (2yz)k and $ is the surface of the plane 2x + y +…

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Q: If A = 18zî – 12j + 3yk then find SS,A.ñds where S is the surface of the plane %3D 2x + 3y + 6z = 12…

A: Given, surface S: 2x+3y+6z=12           and                       A→=18zi^-12j^+3yk^

Q: Compute x dS where S is the portion of the plane z=1+x+2y that lies over the square [0, 1] × [0, 1].…

A: We have to find the surface integral ∫sxds.

Q: In which part of the (x, y) plane the following equation is elliptic? Uzr + 4ury + (x² + 4y*) uyy =…

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Q: (3) Consider the quadric surface SC R, having equation a2 + y? – 22 = 9. Find all lines through P =…

A: The quadratic equation is given by x2+y2-z2=9.  General equation of line is: x,y,z=a,b,c+tl,m,n…

Q: Consider the surface S: Z=4x²+5y?, an equation of the plane fangent to S fhe point P(-2,1, 21) is…

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Q: Calculate f((5x + 2y)i + (4x + 7y) 3) · dr where C' is the circular path with center (a, b) and…

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Q: Let Y be the portion of the sphere x² + y² + (z − 2)² = 4 which lies below the plane z = 3 with…

A: Given  ∫Cz2+3yi→+2z-2xj→+z2k→.dr→ The portion of the sphere x2+y2+z-22=4 and plane z=3

Q: Find the projection in the ry plane of the curve of intersection of the surfaces 222 = r² + y? and r…

A: Find your answer below

Q: Use Divergence Theorem to evaluate [0²z?i+z?x²j+x*y²k).ds, where S is the upper part of the sphere…

A: To evaluate the below integral using the divergence theorem. ∫∫Sy2z2i+z2x2j+x2y2kds Here S is the…

Q: Calculate fc((3x + 5y) i + (3x + 4y) j) - dr where C is the circular path with center (a, b) and…

A: According to the greens theorem:

Q: b. Describe the rigid motion(s) that would map AUVT onto ASVR.

A: Triangle SVR is congruent to triangle UVT by SAS congruence rule as per a. part. Four types of rigid…

Q: Prove that the distance d from a point P (xo, Yo, 2o) to the plane r: Ar + By + Cz + D = 0 is given…

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Q: 28. Show that the ellipsoid 2x² + 3y² + z² = 9 and the sphere %3D x? + y? + z? - 6x – 8y – 8z + 24 =…

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Q: Calculate fc((7x + 6y) i + (4 + 7y) j) · dr where C is the circular path with center (a, b) and…

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Q: Find all points on the surface xy - z2 = 1 which are closest to that origin. Let x,y,z be the…

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Q: Consider the surface S: z = 4x2 + 2y2 . An equation of the plane tangent to S at the point P (−1, 2,…

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Q: Let S be the closed surface composed of the parabaloid z = x² + y? and the planes z = 2 and z = 4.…

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Q: If a parametric surface given by ri (u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -3 <u < 3, –4 < v<…

A: We solve this

Q: a) Evaluate ds, where the curve C is the intersection between the surface z = V1- y? and the plane r…

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Q: Sketch or describe the surfaces in R³ determined by the equa- tions in Exercises 40–46. z = y? + 2

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Q: b) Use Stokes' Theorem to evaluate fF•dr for F(x,y,z) =-yi+ xz j+ zk where C is the curve of…

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Q: 3. Show that every sphere through the circle x2 +y-2ax+r²=0, z=0 cuts orthogonally every sphere…

A: This is a co-ordinate geometry problem

Q: b) Use Gauss' theorem to evaluate SS F · ndS where F = (x² – y)i + y°z²j+ (xy – yz³)k and o is the…

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Q: 17. F = |r|r, where r = xi + yj + z k, S consists of the hemisphere z = /1 – x² – y2 and the disk x?…

A: The solution are next step

Q: Find the extreme values of ƒ(x, y, z) = x2yz + 1 on the intersection of the plane z = 1 with the…

A: consider the following equations  f(x,y,z)=x2yz+1                                  (1)h(x,y,z)=z-1…

Q: Exercise 7.2.8. Apply Stoke's theorem to find F - dr, where F = yi+zj+ækover the surface S, %3D…

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Q: (b) Use Stokes' Theorem to evaluate (f, curlF .n dS, where F(x,y, 2) = x²yzi + yz?j + z³e™Yk and S…

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Q: 8. Let S be the part of the sphere r² + y² + z² = 2 where y 2 1, oriented away from the origin. (a)…

A: Given x2+y2+z2=2 where y≥1

Q: Evaluate Sſ Ands where A= (x+y*)î – 4xj +4yzk and s is the surface of the plane, 2x+y+2z=8 in the…

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Q: a) Evaluate //(-ri-yj+2: k) n dS, where a is the portion of the paraboloid : = 3r - 3y between the…

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Q: (3) Consider the quadric surface S C R, having equation a2 + y? - z2 = 9. Find all lines through P…

A: General equation of line from point 3,-3,3 is x,y,z=3,-3,3+tl,m,n.  Substitute it in the quadratic…