Let (A, B, C, D) be an ordered quadruple of distinct collinear points in II. Let G = S4((A,B,C, D)) = {(A, B, C, D), …, (D,C,B,A)} be the set of all possible ordered quadruples which can be formed from the set of points{A,B,C,D}. ... Prove that that there are six subsets of G which each contain four elements whose cross ratio is equal.

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: 6. Is the set S {(2, 3, 1), (1, 2, 1), (-2, 3, 3)} C R³ linearly %3D independent or dependent?…

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Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the plane through U, V, and W, expressed in…

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Q: Let U(9, 9, 2), V(9, t, 4), and W(2, 5, 8). U, V and W have the same starting point. find t for…

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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: Let R denote the rectangle with corners (−1, −2), (4, −2), (4,1), and (-1,1), and let P denote the…

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Q: If the plane contains the points P(1, 0, 0), Q(3, 2, 0), R(0, 2, 1), W(a, 1, ), then a = -6 O-2

A: Solution: The equation of plane passing through points P1,0,0, Q3,2,0, R0,2,1 is x-y+3z-1=0

Q: Let A be the plane containing the points P(2,2,2), Q(2, 1,3 ) and R(3,1, 3) . (a) Find the equation…

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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: Find the plane through P = (4, −1, 9) containing the line r(t) =〈1, 4, −3〉+ t〈2, 1, 1〉.

A: The plane contains the line r(t)=1, 4, -3+ t2, 1, 1, so a vector in the plane is 2, 1, 1. The line…

Q: A line, in R³ which passes through the point (xo, yo, zo) and with the direction vector (a, b, c),…

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Q: 3. Determine the intersection (if any) of the following planes. Show your work clearly ₁: 2x + 3y z…

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Q: The point on the plane 2x+y+z=1 that is closest to the point (1, 2, 3) is (a, b, c). Then a+b-2c= O…

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Q: Let a be a real number such that a opposit to 0 . An equation of the plane passing through A…

A: Given data:- Plane passing through the points, Aa,-a,-aBa,0,2aC-a,-a,-5a

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: Sketch the set X = [1, 3] × [1, 2] on the plane R . On separate drawings, shade in X ∩([0,2]×[0,3]).…

A: Sketch the product X = [1, 3] × [1, 2] on ℝ.

Q: The point (-2,0,8) is. A. In die xy-vlak O In the xy-plane B. In die yz-vlak O In the yz-plane C. In…

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Q: Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0)…

A: Given equation of plane ax+by+cz+d=0. The plane ax+by+cz+d=0 will divide the xyz space into two…

Q: Which of the following is a point on the plane with equation n = (-3, -2, 2) + t(2, 2, -2) + s(1,…

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Q: nt of intersectic -6 y + 8 = 3 O) カー

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Q: Use Lagrange Multiplier to find the Point P (x,y,z) closest to the origin on the plane containing…

A: The equation of the plane passing through the three points can be obtained using the matrices. The…

Q: Suppose v,, v,,V3 are distinct points on one line in R" . The line need not pass through 29 the…

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Q: 25. Let A = (2, 3, 5) and B = {x, y}. Let p, and p, be the projections of A x B onto the first and…

A: Given that A={2,3,5} and B={x,y} Also given that  p1 is the projection of A×B onto the first…

Q: the planes through A,B and C parallel to the planes x=0 and y=0,z=0 respectively, intersect at Q,…

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