8) Given z =f (x.y) =1- (x² +4y2) ,Find : a)The vector function, 10 normal to the surface of f at (x,y).

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A: Given equation of plane is 5x-5y-z=-10.want to find:Normal vector n to given plane.

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Q: Sketch the space curve represented by the intersection of the surfaces           x2 + y2 + z2 = 16,…

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Q: The vector (x, 2y, –3z) is normal to the surface x2 + 2y? – 32 – 4 = 0 at any point (x, y, z). - - -

A: Let's find.

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Q: Find a vector normal to the surface x2 + yz = 5 at (2, 1, 1).

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Q: The spherical equivalent of the vector B = yi + (x + z)j located at (-2,6,3) is given by

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Q: Find a nonzero vector normal to the plane z − 5(x − 1) = −2(3 — y). - -

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Q: (b) Solve the electric flux through a paraboloid z = x² + y² – 16 that lies below plane %3D z = 0.…

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Q: Find a nonzero vector normal to the plane z−3(x−4) = −4(1−y) correctly.

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Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

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