If A = 18zî – 12ĵ + 3yk then find Jſ, A.ñ ds where S is the surface of the plane %3D 2x + 3y + 6z = 12 in the first octant.

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A: The solution is given in the next step.

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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: Consider the surface z = (x+ 1)² + (y – 2)² – 1 Does the point (1, 3, 1) belong to this surface?

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Q: (b) A = 2pza, + 3z sin ø a, – 4p cos p a̟ and S is the surface of the wedge 0 0 < ¢ < 45°, 0 <z < 5

A: Let us solve the b part step by step with given A value

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A: Given : The surface 1 - x = 3y2 + 4z2   To classify the given surface.

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Q: Find the points on the surface represented by x2 + y? + z2 - 4x – 6y + 2z = -10 which are closest to…

A: To find - Find the points on the surface represented by x2 + y2 + z2 - 4x - 6y + 2z = -10 which are…

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: Identify the quadric surface satisfying each of the given equations and then make a rough sketch to…

A: identify the quadric surface satsifying each of the given equations and make rough sketch to show…

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Q: 1. Consider the following equation of a quadric surface. z=x2+ 169y2 a. Find the intercepts with the…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

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: The value of . (x² +y²) dS, where S is the surface of the paraboloid z = 2- (x² + y2 ) above the x-y…

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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: Find the surface area of the plane ( 15x- ? 5z+20y=D35) if it is in the first octant

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Q: Sketch the surface z = 3x? + y? +1 and find its linear approximation at P-(0, -1)

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Q: Let (P) be the surface given by the following equation z = 5-x²-y² and (Q) be the surface given by…

A: Given surface P is, z=5-x2-y2    ----(1) For xy projection, put z=0 in (1) we get, 0=5-x2-y2⇒…

Q: Find the area of the surface of the part of the plane 3x + 2u + z = 6 that lies in the first octant.

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Q: Sketch the surface r = 2y? + 32².

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Q: The surface 22 = x² +y? – 4x + 5 remains unchanged when rotated about the line L in R³ Which of the…

A: The given surface is z2=x2+y2-4x+5, which is as shown below: This is a hyperboloid paraboloid.…

Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y° + = 288 and the paraboloid…

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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: If a parametric surface given by r1(u, v) = f(u, v)i + g(u, v)j+ h(u,v)k and –1< u<1, –2 < v< 2, has…

A: We will find out the required value.

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Q: Given the planes 3.x – 6y – 2z = 15 and 2x + y – 2z = 5 anser the following. (b) Find parametric…

A: I have solved using an intersection point and direction ratios

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Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y² + z? = = 24 and the…

A: We have to write the intersection curve

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Q: Let E be the region in the plane between the two ellipses 4x² +9y? = 1 and 4x2 + 9y2 = 4. Evaluate…

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Q: Find a generating curve on the xz-plane for the surface of revolution with equation x2+ y²+ z²= e2x…

A: The solution is given below

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Q: Which of the following is an equation of a plane surface? O 2x +3y + 4z = 4 O 2x2 +3y + 4z = 4 O 2x…

A: To find:- Select an equation of plane surfacefrom given options

Q: Find an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^2)…

A: Solution

Q: Find the traces for the given surface: 16x? +16y² – 9z = 0. Then sketch and identify the surface.…

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Q: Find the surface area of the plane ( 15x-5z+20y=35) if it is in the first ? octant

A: Solution

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Q: Identify the following surfaces as an elliptical paraboloid, hyperbolic paraboloid, a hyperboloid of…

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Q: Let 11 be the surface with the equation = 2√y+1 and let 12 be the sphere with equation x²+y+z² 16x +…

A: Given data÷ Find the center and radius of the sphere   x2+y2+z2-16x+16y-4z+76=0   General form of…

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Q: Find the area of the surface of the part of the plane 3x + 2y + 4z = 2 that lies inside the cylinder…

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Q: Use traces to sketch and identify the following surface 25x2+4y2+z2=100

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