Find the perpen dicular trajec ories of the plane faimily its intersection X -y +2 = Ł Cヒ cons tan+) and the (x +y)2 = ! Surface. curves on

Q: Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point…

A: We will find shadow of given points on the plane given and then find parametric equation of the line…

Q: For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which…

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Q: Liad para mean'c ecquation foo line 6f intersecton of planes 21-4+Z=4 3x +y + Z =l

A: Solution: The objective is to find the parametric equation for a line of intersection of planes…

Q: y at (1,1,1)

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Q: Consider the paraboloid z = a? + y. The plane 10x – 4y + z – 2 = 0 cuts the paraboloid, its…

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Q: Find a point on the ellipsoid x + 3y² + z = 8 where the tangent plane is perpendicular to the line…

A: Introduction: The perpendicular vector to a 3D object f ( x, y, z ) can be calculated by computing…

Q: Find the regions of the (x, y)-plane where the equation ey. + e*. dxðy + 2e2". +x³. + e*-Yu = 0 ду |…

A: The given PDE is        ey∂2u∂x2+ex∂2u∂x∂y+2e2x∂2u∂y2+x3∂u∂x-(x+y)2∂u∂y+ex-yu=0. A second order PDE…

Q: Consider the surface O3z+3y-2z=0 O 34z + 7y-12z = 0 O 3x+3y-2z=147 What is the equation of the…

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Q: Match each parametrization with the corresponding surface. (i) (ii) (iii) (iv) (v) Answer Bank (u,…

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Q: Determine the parametric equations of the curve of of the ellipsoid 4x² + y2 + 4z2 = 4 and the…

A: Solution: Given equation:ellipsoid: 4x2+y2+4z2=4; and half−cone: y2=x2+2z2 To find: parametric…

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

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Q: Determine parainetric cquations for the line L representing the interscction of the planes x – y +…

A: Given equation of plane are:-           x - y + 2z = 0 and             3x + y - z = 1

Q: Find an equation of the plane that contains point A(5,1,1) and the line that is given with…

A: Please see the below picture for detailed solution.

Q: Q3: Find the distance between the origin and the plane containing the points A(1,1,0), B(-1,0,1) and…

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Q: (a) Find the equation of the plane containing the lines. x=2+t Ly=3-2t |z=1-3t x=1+3s L₂y=1-2s z =…

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Q: a) A curve can be parametrized by calculating its intersection point with the line y = tx, in which…

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Q: Consider the function f(x, y, z) = 3x² + y² - 4z. i) A contour surface S passes through the point A…

A: To find the value of the contour surface passing through the point A = (2, 3, -1), we need to…

Q: Consider two non-parallel lines L1 and L2 in R2 with the following parametric equations: (3,6) +…

A: Given : L1 = (3, 6) + s(3, -4) and                   L2 = (-4, -6) + t(2, -4)

Q: (a) Graph u in the coordinate plane, with initial point (0, 0).   (b) Find the length and direction…

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Q: with the guldin's proposition 1 get the contents of the rotating object that occurs if the land…

A: As per the question we are given a 2d region bounded by the curve : y = 6 - 3x - x2 and the straight…

Q: Consider the curve r(t) = (a) Pick any three points along the curve. Then find an equation of the…

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Q: Let S be the quadric with equation 36x² –4y² –9z² – 36x = 0. Sketch a graph of the surface with…

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Q: Find the equation of the tangent plane to the surface of the equation z = x2 + y2 - 2xy on the point…

A: Equation of tangent plane

Q: y² - (z²/3) = 1 + (x²/12) sketch the quadric surface. emphasize the traces on the coordinate planes…

A: Given a quadric surface y2-z23=1+x212. YZ trace: When x=0, we get y2-z23=1. This is a hyperbola on…

Q: arameterize the intersection of the plane x = 1 and the surface z = x2 - 2x2y + y2.

A: To parameterize the intersection of the plane x = 1 and the surfacez=x2−2x2y+y2, we can set x = 1 in…

Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…