Show that (u, v) = (6u + 6, u – v, 1lu + v) parametrizes the plane 2x – y – z = 12. Then: (a) Calculate Tu , T, and n(u, v). (b) Find the area of S = ¢(D), where D = (u, v) : 0 < u < 4,0

Q: Parameterize the intersection of z = - Vx² + 7y² _and x² + y? + z? = 200

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Q: Find a parametrization of the line in which the planes x- 2y - 2z = 3 and -3x + 3y + 3z = -6…

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Q: Define diffeomorphish between two manifolds and Completly explain why any linear map fiM_N. between…

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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: A car costs x wholesale. The price the dealer pays is given by the function s(x) = = x-1 – 200 where…

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Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

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Q: The scalar component of H parallel to the line y=1, z=2 where H = -2a, + 3as- 4a, at p (1,90, 2) -3…

A: Given: H=-2aρ+3aϕ-4az p=1,90,2

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Q: Parametrize y = -x2 + 4 in terms of u and v %3D

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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: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

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A: Solution :-

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.