Find a parametrization of the line in which the planes x- 2y - 4z=1 and - 2x +3y + 6z = - 3 intersect. Find the parametrization of the line. Use a point with z = 0 on the line to determine the parametrization. X = |, y = ,z= - o

Q: 2. Prove that fo r*dr + xydy = -+- where C2 is the line segment from (1,0) to (0, 1) by using…

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

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Q: Find parametrizations The portion of the hemisphere x2 + y2 + z2 = 10, y>= 0, in the first octant

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Q: Find all points on the ellipsoid 2x² + 3y² + 4z² = 9at which the plane tangent to the ellipsoid is…

A: Explanation: Given that,  Ellipsoid:2x2+3y2+4z2=9Plane:x-2y+3z=5⇒15x-25y+35z=1   Suppose point of…

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A: Modify the given figure as shown in Figure 1.

Q: (b) Give an example of a parametrisation of the unit circle, C = {(x, y) E R² | x² + y² = 1}, that…

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A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Write down a parametrization r(u, v) for the portion of the plane x - y+ z = 3 that lies inside the…

A: r(u, v) = ( u cos v , u sin v,  3 - u cos v + u sin v)  Where u € [0, 1]           v€ [ 0,2π]

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Q: Find a parametrization for the portion of the sphere x2 +y2 + z2 - 16 between the planes z =- 2/2…

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Q: A point moves along the intersection of the elliptic paraboloid z = 6r + 7y and the plane y = 2. At…

A: Given: A point moves along the intersection of the elliptic paraboloid z = 6x2 + 7y2 and the plane y…

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Q: Find a parametrization for the line segment from 2₁ =1-i to Z₂ = 2i. A. 2 (t) = 1 -i + (−1+3i) t 0…

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Q: : The curve C is intersecting by 12r² +9y? = 36 cylinder and - V3r plane from the point (0, 2,0) to…

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A: Let First, find the tangent planes at (1, -1, 0), (1, 2, 9).     Tangent plane at (1, -1, 0):…

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Q: Find a parametrization of the line in which the planes x + y+z= - 1 and x+y=4 intersect. Find the…

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Q: The tangent plane to the elliptic paraboloid z = -2x - 7y? at the point (-3, -4) is

A: Consider the provided question, The equation of the tangent plane to the elliptic paraboloid at the…

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Q: Bounded by the paraboloid z = 10 – 3x? – 3y2 and the plane z = 4 (using polar coordinates)

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Q: Find a parametrization for the intersection of the surfaces: z = x2 + y2 and  x2 + 4y2 = 1

A: Find the parametric representation for the intersection of the given surfaces.

Q: Let C CR be the curve from (0,-7,0) to (-2,-3,-8) along the intersection of the surfaces x- y 7 and…

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Q: Find a parametrization for the line segment joining points (0, 2) and (4, 0) using the angle 0 in…

A: Given: The line segment joining (0, 2) and (4, 0). Do the construction as in below figure