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

Q: 1. Prove that fo r*dr + rydy = where C1 is the line segment from (0,0) to (1,0) by using…

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Q: Find a parametrization for the cylinder x2 + y2 = 1.

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Q: Find parametrizations for the lines in which the planes x + y + z = 1, x + y = 2

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Q: Let L denote the intersection line between the planes 2x-y-3z=4 and 2x+y-z=2 A) Determine a…

A: Solution of the system of equation will give the equation of the line of intersection.

Q: Find the moving tri hedral of f R CE) = t, 2E> at %3D

A: This is a problem of differential Geometry.

Q: find a parametrization for the curve. the left half of the parabola y = x^2 + 2x

A: First, we will find the symmetric line of the given parabola y=x2+2x. We know that the symmetric…

Q: Find the angle between the two planes 6x − 3y + z = 5,  −x + y + 5z = 5 and find a set of parametric…

A: We have given the equation of planes; 6x − 3y + z = 5 −x + y + 5z = 5 Hence the normal vectors of…

Q: parametrizes the portion of the sphere x² + y² + z² = 9 that is above the xy-plane and below the…

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Q: Find parametrizations The portion of the plane 4x + 2y + 4z = 12 that lies above the square 0<=…

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Q: Find a parametrization and the equation associated with the cylindrical surface whose directrix and…

A: Use the director vector and then substitute y=0 to find the value of x and z . Then substitute the…

Q: and the plane - 3 X + Z Intersect along a line. Find Parametnic desenetion of this la

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Q: Give a parametrization, including the appropriate u- and v-bounds, for the portion a cylinder of…

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Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2,4) and (-…

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Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x-2y+z = 4.

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Q: Find a vector parametric equation for the ellipse that lies on the plane 5y−3x+z=9 and is inside the…

A: Given that: 5y-3x+z=9 Let x=u cos v, y=u sin v So z=9+3x-5y  =9+3u cos v-5u sin v

Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

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Q: Find a parametrization of the hyper-boloid of two sheets (z2/c2)-(x2/a2)-(y2/b2)=1

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Q: Use the method of Lagrange multiplier to find the 3D vector lying on the intersection of hyperplanes…

A: let u=x i+y j+z k be a 3D vector lying on the intersection of hyperplanes x+y=2 and y+z=4 that has…

Q: Find a vector function that represents the curve of the intersection of the two surfaces. The…

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Q: /Sketch the Surface Z=V9-X+y- and verify that fxg = Exx %31

A: Second order Partial Differentiation

Q: Find a parametrization for the sphere of radius 2.

A: Consider the equation of the sphere x2+y2+z2=22. Here the sphere is centered at origin.

Q: Find the Parametrization of the line.

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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: Modify the given figure as shown in Figure 1.

Q: Find a vector parametrization for the intersection of the plane x + y+z = 3 and the cylinder x² + z2…

A: solution given below..

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

A: The parameterization of a circle  that generates the clockwise orientation of C is given by: x=r…

Q: Find a parametrization of the circle of radius 6 in the XY-plane, centered at the origin, oriented…

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Q: the trace of the surface in the plane x=1?

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Q: . Find a parametrization for the circle (x – 2)² + y² = 1 starting at (1, 0) and moving clockwise…

A: Consider the equation of circle

Q: Find all points on the isometric dot plane, Ax,1 yl, with x and y integers, that are ex- actly V133…

A: a)The distance from origin to point x,y is 133. b)The distance from origin to point x,y is 217.

Q: Find a parametrization c(θ) of the unit circle such that c(0) = (−1, 0).

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Q: Find the angle between the two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2 and find a set of…

A: Given, two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2  we have to find the angle between the two…

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]

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

A: we have been given a sphere x2+y2+z2=16 between the planes z=-22 and z=2

Q: 5 Find a parametrization for the line segment joining the points (0, 2) and (4,0) using the angle in…

A: A parametrization for the line segment joining the points (0,2) and (4,0) using the angle θ in the…

Q: Find the orthogonal trajectories of the conicoid (x + y)z = 1 of the conics in which it is cut by…

A: Given:The equation of conicoid is (x+y)z=1The system of the plane is x-y+z=K, where k is…

Q: Use a parametrization to find the flux F•n do of F = 5zk across the portion of the sphere

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Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…

Q: Find the distance between two planes a and a1 that are tangent to the ellipsoid 2 +2y? + z² = 5/8…

A: We have to find the distance between the two tangent planes parallel to x+y+z=0  that are tangent to…

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

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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…

Q: Find a vector parametric equation for the ellipse that lies on the plane z (x + 2 - cylinder x + y =…

A: Dear student. You have posted many parts, according to the policy we will answering the first part.…

Q: Find parametrizations The portion of the paraboloid y = 2(x2 + z2 ), y<=2, that lies above 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: Flnd the parametric equation of the line of ntersection of the planes and

A: First find normal vector then take cross product and use formula

Q: Find the parametrization for the curve  the lower half of the curve x+3=y^2

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Q: Find a vector parametrization for the quarter-ellipse from (5, 0, 6) to (0, −2, 6) centered at (0,…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.