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: Find a vector function r(t) that describes the curve of intersection be- tween the elliptical…

A: Given To find a vector function r(t) that describes the curve of intersection between the elliptical…

Q: Let C = (-2, -1) be the center of dilation. Let X = (1, 1), Y = (3, 0) and Z = (2,5). Our dilation…

A: Center of dilation=-2, -1X=1, 1, Y=3, 0, Z=2, 5Dilation factor, k=3

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

A: To find the equation of line with parameter t of the intersection of the planes  x + y + z =4 and…

Q: Consider the following function. T: R2 - R3, T(x, y) = (2x², 3xy, y²) Find the following images for…

A: Let us consider the given transformation T:V→W then the transformation is said to be linear…

Q: Let l be the line y = - (7x + 5) in R21 Find vectors dland b so that v = a + tblis a parametric…

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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..

A: Any arbitrary point P0 on the line can be determined to be as:

Q: Find the distance from the point (1,1,1) to the plane 2x+2y+z=0

A: Solution :-

Q: 285. Find the scalar equation of the plane that passes through point P(-1, 2, 1) and is…

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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.