Let F(x,y,z) = ztan(y2) i + z³In(x² + 4)j+z k. Find the flux of F across the part of the paraboloid x2 + y2 + z = 6 that lies above the plane z = 2 and is oriented upward.

Q: Let Z = (1, 1, 2) be a point in R³. Find the closest point to Z tha lies on the plane give by -x+y-z…

A: The normal vector to the plane is <-1, 1, -1>. The point you seek would have to be some…

Q: Find the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

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

A: Introduction: According to Green's Theorem, a line integral of a vector over a closed curve C…

Q: Find a vector function that represents the cur ve of intersection of the paraboloid z a + mnd the…

A: Given that, the paraboloid is z=x2+y2 and the cylinder is x2+y2=22. The projection of the of the…

Q: Consider the plane with a scalar equation 4x-2y+z-19=0. Find the point of intersection of this plane…

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Q: Find a scalar equation of the plane containing the line x = 4+ 5t, y = 5+3t and z = 6+ 4t the point…

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Q: Determine the scalar equation of the plane that contains A(-1, 3, 1) and is perpendicular to both 5x…

A: The normal vector of a plane is a vector that is perpendicular to the plane. The coefficients of x,…

Q: Find a vector parametric equation for the ellipse that lies on the plane 4x - 4y + z = -7 and is…

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Q: Find the scalar equation for the plane passing through the points P1(2, 1, 5), P2(2, 0, 9), and…

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Q: Let C be the rectangle in the xy-plane with vertices (0,0), (1,0), (0, 2) and (1, 2), and let F(r,…

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Q: Consider the following function. T: R2 → R?, T(x, y) = (x, 5) Find the following images for vectors…

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Q: Let L be the line passing through the point P(1, -1, -2) with direction vector d=[3, −4, 0]T, and…

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