3. Let D = {(x, y, z) | x² + y² ≤ 1, z = 0.} C R³ be the unit disk in the xy-plane. Is D a Jordan Domain in the xy-plane as a set in R²? Does D have Jordan content 0 as a set in R²? Is D a Jordan Domain in R³? (What is the boundary of D in R³?) Does D have Jordan content 0 as a set in R³? Justify your statements.

Q: B- Consider the following subsets of real plane R² Determine with graph: 1- Arcwise connected A =…

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Q: Let P and Q be points in R2. Show that a linear map G(u, v) = (Au+ Cv, Bu+ Dv) maps the segment…

A: Let P and Q be two points in R2. We have to show that a linear map G(u, v) = (Au + Cv, Bu + Dv) maps…

Q: C, D are coplanar points. A', B', C', D' are their projections respectively on the y-

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Q: What is the point of intersection of the following line and plane: line: 7 = [3, 1, 2] + t [1, - 4,…

A: Given  r⇀=3,1,2+t1,-4,-8& plane π=4x+2y-z-8=0 To find point of intersection:

Q: 3) A vector is given as A = x(z+2)â,-()x+1)â, +(y+2)â. Prove the Stoke's theorem for the geometry…

A: From the below figure, ∮cA.dt=∫ABA.ds+∫BCA.ds+∫CDA.ds+∫DAA.ds Here ax=i, ay=j, ak=k Since…

Q: A plane is perpendicular to [x, y, z] = [3, -30, 24] + s[2, 4, -2] and contains the point…

A: Step 1:​Plane is perpendicular to [x,y,z]=[3,−30,24]+s[2,4,−2]Direction of Line…

Q: Find the distance between the parallel lines in each pair. a) l₁: [x, y, z] = [2, 5, 4] + [2, 1, 3]…

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Q: The surfaces intersect in a space curve C. Determine the projection of C onto the xy-plane.…

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Q: Calculate ff f(x, y, z) dS, where S is the part of the plane x + y + z = 2, where x, y, z ≥ 0, and…

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Q: 4. Prove that these lines are contained in the same plane. [x, y, z]= [1, 4, 0] + s[-2, 1, 3] [x, y,…

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Q: 1. a) Compute the point of intersection of the two lines ₁ (t) = (2+ t, 1 + 2t, 5 + 3t) and r₂(t) =…

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Q: Let a and b be real numbers. Let L be the line defined as L: æ = 6 – 6t, y = -11+t, z=a + bt, te R…

A: Suppose P : Ax+By+Cz=D is a plane and L: x-x0a=y-y0b=z-z0c=t is a line .If L is parallel to D then…

Q: The distance between the point P(x₁, y₁, 2₁) to the plone with equation Ax+By+ (z+D=0 is equal to |…

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Q: Is a subset of the plane {(x1, x2); x1 > 0, x1x2 ≥ 1} convex? Justify.

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Q: Let R = (c, 1,-1) where c denotes a real number. Let ä denote the plane x + y – z = 2. Find the…

A: Given Information -  The distance from the point R = (c,1,-1) to the plane x+y-z = 2 is 2. We have…

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: Find a plane containing the lines x = 3+ 21 x =1- 21 y = 4– 31 and y = 7+41 where -o <t<00, z =1-31.…

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Q: Let P(V) be a projective space of dimension > 2, and let [v], [v2), [v3] € non-colinear points…

A: A common definition of "projective plane" includes the following axioms: every pair of distinct…

Q: ) fnd the equ. f Plane that Contains the two line S: X-1=3+ 6=そ X-リ=Z-4 and Passes through origin?…

A: Given problem:- find the equation of Plane that contains the two lines x - 1 = y + 6 = z ,    x= y =…

Q: Apply Gauss's theorem to evaluate. A

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Q: 11 What restrictions must be made on x, yond z X, So that the triple (x, y, z) will represent a…

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Q: Show that the cartesian plane R² is a Euclidean plane and an affine plane

A: We need to show that a Cartesian plane is also affine plane. An affine plane can be defined as…

Q: Do the following task. a)  State formally what do mean by being an open set of E in metric space…

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Q: In space coordinates, the xy plane consists of all the points of the form O (0, y, z) O (X, y, z) O…

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Q: 9. Suppose that a : R³ → R³ by perpendicular projection onto the plane 3x – 2y + z = 0. Find ↑

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Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

A: Surface integral

Q: Consider the following subsets of real plane R termine with graph: Arcwise connected A = ((x,y): 0 ≤…

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