Consider the Euclidean plane, and instead of ordinary lines, let the line segments PQ for all pairs of distinct points P, Q be taken as the “lines.” Show that this system of points and lines satisfies Axioms 0–2. What seems unnatural to you about this geometry?

Q: GRO 5. Consider the infinite set of positive integers {1, 2, 3,..}. Find a way to name definite…

A: Consider the infinite set of positive integers.

Q: Given the following points A, B, C and D, which of the vectors and are parallel? CD (a) A= (1, 2),…

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Q: .Find the equation and sketch the plane that contains the points (2, 6, 1), (-4, 9, -1) and (4, 3,…

A: Equation of plane is 3x+2y+6z = 12

Q: Find the point at which the given lines intersect: r = + t r = + s

A: I think the equation of the first line is Thus, the parametric equations of two lines are x = 3 +…

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

Q: 20. Determine the angle between a = (5, 3, 0) and b = (-1, 0, 8) 21. The vertices of a quadrilateral…

A: Step 1: In order to determine the angle between a=(5,3,0)&b=(−1,0,8) lets use the dot product…

Q: The distance between the line P(t) = (-4,-3,-5) +t(1,0, 2) %3D and the line Q(t) = (-3, -4,0) +t (2,…

A: The vector equation of a line passing through a point with position vector a1→ and parallel to a…

Q: 9. Prove, by coordinate geometry that QRST is a parallelogram. Q(0

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Q: a) Show that the lines х — 3 у — 2 x + 1 у — 2 z - 5 аnd %D 2 Intersects and find the point of…

A: Given that:                        Equation of lines: x-3-1=y-2-3=z2…

Q: Are the following statements true or false? If true, explain why. If false, provide a counter…

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Solve the following problem and explain your answer for better understanding. Given a set of points…

A: In a projective plane, any two distinct points can be connected by exactly one line. Since no three…

Q: Answer the questions in detalied steps and show work. (7 and 8)

A: Step 1: Step 2:   Take x-axis and y-axis                 they intersect at (0,0) in two-space and…

Q: Let A be the point with coordinates (0, -4, -1), let B be the point with coordinates (4, 0, 1), let…

A: The objective is to find the x-coordinate of point P.

Q: The midpoint of a segment can be found using the formulas for a directed line segment, x = (X2-X1) +…

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Q: 33. Sketch the diagram that you would use to find the magnitude of the sum of a and b if the angle…

A: 20. To find the angle between two vectors \(\vec{a}\) and \(\vec{b}\), you can use the formula…

Q: A.If angle ABC has vertices A(3,6) B(-2,-3) and C(8,6) what would the coordinates under the…

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Q: If l,, l2, and l3 are nonconcurrent lines, prove that there exist three points. Exactly one each…

A: Three or more points are said Lto be collinear if they all lie on the same straight line If l1 , l2…

Q: Here let A, B, C, and D be four distinct points in the plane. Now supposedly that no three of them…

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Q: ) Find an equation of a line that is perpendicular to both u = and v m and contains the point (2,3,…

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Q: a. Draw the affine plane, AG(2, 3). b. How many points are in AG(2, 3)? How many lines? How many…

A: To determine:a. Draw the affine plane, AG(2, 3).b. How many points are in AG(2, 3)? How many lines?…

Q: 1. Let points A, B, C, and D be as follows: A=(3, 1, 2), B=(-1,3,5), C= (0, 2, 2), D =(4, 5, 1) a)…

A: The distance of a plane is defined as the algebraic expression that gives the pairs of points in the…