Prove an isometry on C maps parallel lines to parallel lines without using the geometric concept of equidistance. (You may use that two lines are parallel if and only if they both are translations of the same line through the origin.)

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Q: . For what values of a are the points (6, 2, 3) and (a, 2, 5) and the line = (2,-1,-2) + t(3,1,-2)…

A: I have appended the formula used in the solution part of the question

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Q: Let a and m be real numbers, u = (1, a, 2, m, -3), and w = (2, а, 2, т, 3). Then the distance…

A: Let's find.

Q: pai (S-.I.S)+(1,0,5) =3 bimsnq omami i 3. We are given lines = (7,0, 1) + X(2, 1, -2) and q: x + 3 =…

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Q: Through any point (x, y) of a certain curve which passes through the origin. lines are dawn parallel…

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A: Given:

Q: marked on the plane, any three of which were not collinear. These points determined 36 straight…

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Q: Which of the following statements is/are true about non-Euclidean geometries? I. In non-Euclidean…

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Q: Let P(6, – 2, 2) and Q(0, 0, 0) be two points in R³. Find the distance between P and Q. - PQ

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Q: Ex 12.8. Let S be a set of q + 2 points in a projective plane of order q. Prove that every line,…

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Q: (a) Show that point points i, 2i, 4i, 8i, 16i,... are equally spaced along the upper y-axis in the…

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Q: Prove that a line cannot contain three distinct points.

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Q: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

A: Prove that if the points (x1, y1) and (x2, y2) lie on the same line as (x∗1 , y∗1 ) and (x∗2 , y∗2…

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