Q2. In the model R³ of the Euclidean Geometry E.G., let 0(0,0,0), A(-2,2,0), B(2,2,0). Then the convex Hull of the set n= (0,A,B) is: A) {(x,y,0):-y≤x≤y, Osy≤2} Β) Ω C) {(x,y,0): -ysxsy, 0

Q: Does the sphere x + y + ? = 25 have symmetry with %3D respect to a) the xy-plane? b) the line e: (x,…

A: we have the sphere x2+y2+z2=25  here the radius is 5

Q: Let l,,l2,lz be the lines X(t) = (1,1, 2) + t(1,2,3), X(s)= (9,8,11) + s(2,1,1) and X (r) = (0,0,0)…

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Q: III) Suppose that the linear map T: R-R' satisfies 00 0-0-0-0-0-0 2 2. What are det T and trace T?

A: Given :-  Suppose that the linear map T : ℝ4 → ℝ4 satisfies T 1000 = 2622 ,  T 0100 = 1311 ,  T 0010…

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

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Q: (2,3) is te i చాంబ! Under a ro dediona Identidy three distinct point that Cald be the center & of

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Q: Find a vected that is Perpenditular to the Plane that Contaiins the e poin +s P(2,3,4), Q~2)0,5), R…

A: Given: The three points:  P (1 , 3 , 4 ) , Q ( - 1 , 0 , 5 ) and R ( 4 , 2 , 2 ).   To determine: A…

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: u" - 16u = 0

A: Given the differential equation is u" - 16u = 0. Here the auxiliary equation is m2 - 16 = 0

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: using green's theorem calculatefx'd +(4x + y ky ,where c is the vertex of the triangle (0,0),(1,2)…

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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: Evaluate da where T is region in the xy-plane enclosed by the Trapezoid T with vertices at the…

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Q: 9. Let E be the tetrahedron with vertices: (0,0,0), (3,2,0), (0,3,0), (0, 0, 2). E is bounded by…

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Q: Prove that the planes determined by the equations ax + by + c z = d and αx + β y + γ z = δ are…

A: Given planes, ax + by + c z = d αx + β y + γ z = δ

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

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Q: Consider the set P= {(x, y) E R² :0 <x< 2 and 1 <y< 2}U{(x,y) E R² : 0 < x <1 and 0< y < 2}. (a)…

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Q: 9.) Let E be the tetrahedron with vertices: (0,0,0), (3, 2,0), (0,3,0), (0, 0,2). E is bounded by…

A: The tetrahedron bounded by the planes              from the plane…

Q: If A (x₁, y₁), B(x, y₂) and C (x, y,) are the vertices of a A ABC and (x, y) be a point on the…

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Q: II1. Recall that using vector projections, we showed that the dis- tance from a point (x1, Y1, 21)…

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Q: Let T be the tetrahedron with vertices (2,0,0), (0, 5, 0), (0, 0, 4) and the origin. Write f(x, y,…

A: The equation of the plane through (2,0,0),(0,5,0),(0,0,4) is x2+y5+z4=1 i.e.,10x+4y+5z=20 For y…

Q: Find the envelope of the plane y Z + u X a + u + + b+uc = 1.

A: Given Data: Let us consider the given data, xa+u+yb+u+zc+u=1 To Find: The envelope of the plane.

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: Let D be the solid tetrahedron in the first octant bounded by the coor- dinate planes together with…

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Q: π be the plane that touches the sphere E with center C= (2,2,2) at the point A=(7,4,2).The line…

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Q: (d) Let (Fn) be a sequence of closed subsets of M, and S, (j = 1,...,5) be subsets of M such that.…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 2-) Calculate the distance d of the pont P(-1,1,-2) through the throe points the plane pu sing from…

A: The distance d of the point p=(-1,1,-2) from the plane passing through the points A(1,-1,1)  ,…

Q: Consider R' endowed with the dot product. Let W = span{u1, u2} where u1 = (1,0, 1) and u2 = (-1, 1,…

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Q: 9.) Let E be the tetrahedron with vertices: (0,0,0), E is bounded by four planes: z = 0, x=0, 2 3…

A: Volume of tetrahedron

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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