Find an appropriate parametrization for the given piecewise-smooth curve in R³. x² + y² 4 16 C(t) = The intersection of the plane z = 8 with the elliptical cylinder for t= [0, 1] = 1.

Q: In what plane does the curve r(t) = t i + t2 k lie?

A: r(t) = t i + t2 k We need to find the plane of the curve located in?

Q: I3D Find the coordinates of the point (x, y, z) on the plane z = 2 x + 2y + 2 whi X = y =

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Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

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Q: The equation z = f(x,y) = y +x -3y defines a surface. What is t- equation of the tangent plane at…

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Q: Find the distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

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Q: Find an equation for the plane that is tangent to the surface z= In (x* +y) at the point P(1,0,0).…

A: The solution for the above question is as shown below.

Q: Consider the plane x-y-z-8= 0. Find the point in this plane closest to the point (1, 0, 1).

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Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…