Using Stokes' theorem, solve the line integral of G(x, y, z) - (1, x + yz, xy-√z) around the boundary of surface S, which is given by the piece of the plane 3x + 2y + z = 1 where x, y, and z all ≥ 0.

Q: Find a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: Find the values of the constants C₁, A such that the function y(x) = C₁e satisfies to ODE with the…

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Q: he vector v = , is tangent to the surface x2 + 2y3 - 3z2 = 3 at the point (2, 1, 1).  Find a.

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Q: c) Verify Stokes's Theorem for F = (x²+y²)i-2xyj takes around the rectangle bounded by the lines x…

A: Stoke's law is given as ∫cF→.dr→=∫s∫∇×F.n→ds F=x2+y2i^-2xyj^ dr→=(dxi^+dyj^) So F.dr=x2+y2dx-2xydy…

Q: Calculate line integral F-dr where F(x, y) = (7x + y, 5x + 2y) and C is a rectangle with vertices…

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Q: ve = Vti + Vrj + (2t – 1)k is tangent to the surface x+y-z = 1 Show that the curv when t=l

A: Consider the given curve r=ti+tj+2t-1k And the given surface x2+y2-z=1 First, write the curve in…

Q: Evaluate the line integral (2x-y+6)dx + (5y + 3x - 6)dy, for which the path C traverses C around a…

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Q: Find a parametrization of the surface x³ + 15xy + z² : = 10 where x > 0 and use it to find the…

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Q: Compute the line integral: y² dx + x² dy two ways. C

A: We have an line integralTo evaluate the line integral by two methods (a) By  Green theorem(b) By,…

Q: Let C be the positively oriented square with vertices (0, 0), (2,0). (2, 2). (0, 2). Use Green's…

A: Green's Theorem:  For a positively oriented curve C∫CP dx+Q dy=∫∫D∂Q∂x-∂P∂y dAfor the region D…

Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…