- Consider noncoplanar points A, B, C, and D. Using three points at a time (such as A, B, and C), how many planes are determined by these points?

Q: 4. Give a geometric description of each family of planes.

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Q: Points A, B, C, and D are coplanar. A, B, and C are the only three of these points that are…

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Q: 1. Consider the finite projective Geometry satisfying the well-known axioms A1-A6 and having two…

A: GivenConsider the finite projectile.Geometry satisfyingthe well known axioms. A1-A6 and havingtwo…

Q: 18. Prove that if A, B, and C are any three distinct, collinear points, then either A-B-C, A-C-B, or…

A: Given A, B and C be three points that are distinct and collinear. Distinct means A≠B≠C and collinear…

Q: Let →a=⟨−2,0⟩ and →b=⟨−5,5⟩ Find the projection of →b→ onto →a (   ,   )???

A: Recall: Projection of b→ onto a→ , proja→b→=a→.b→a→.a→a→

Q: A, B, and C are collinear points: Cis between A and B. If AC = 2x + 1, CB = 3x - 1, and AB = 35,…

A: Given that: A,B,C are collinear points C lies in between A and B

Q: Find the point E that partitions the directed segment CD  in a ratio of 1:5, given the points…

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Q: Find the area of a parallelogram having the vertices P(1, 1, -1), Q(4, 2, 1), and R(6,3,1) O √13 O…

A: To find the area of a parallelogram having the vertices P1, 1, -1, Q4, 2, 1 and R6, 3, 1.

Q: (a) Find the length of the projection of w onto v given that w = (4,7) and v = (1,1).

A: Given: w=4i+7j, v=i+j we know that projectionp→ of w onto v is given by p→=w.→v→v→2v→

Q: Prove that if A-C-D, B-F-C, and A-F-G (all in the same plane) and A, B, and C are noncollinear, then…

A: Given:  ACD , BFC and AFG all are in same plane and A,B and C are noncollinear , then G is the…

Q: e of the parallelepiped with the given vertices A, B, C and

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Q: Suppose that (a) points A, B, and C are collinear and (b) AB > AC. Which point can you conclude…

A: (a) A, B and C are collinear⇒ A, B and C lie on a straight line

Q: If D is the triangle with vertices (0,0), (40,0), (40,25), then dA=

A: The triangle D is with the vertices (0,0), (40,0) & (40,25). The line passing through (0,0) and…

Q: Let a = (- 4, 5) and b = (4, – 3). Find the projection of b onto a.

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Q: Find the point E that partitions the directed segment CD in a ratio of 1:5, given the points C(4,-2)…

A: Given that the line segment  CD is cut by a point (x, y) in the ratio 1:5given that points C(x1, y1)…

Q: 9. Suppose z1, z2, z3 are the vertices of an equilateral triangle inscribed in the circle |z| = 2.…

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Q: Let a = C(7, 4), b = C(7, 5), c = C(7, 6), and d = C(7, 7). If there are 7 points on the plane, no…

A: Solution

Q: How many planes are shown in the figure? *

A: Given geometry is hexagon prism. Hexagon is a regular polygon made up of six edges. When the edges…

Q: Let A=(0, π ) υ (π e?] %3D c. Is A a closed set? d. Does A contain any isolated points? е. Find the…

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Q: 3. Write the (a) center, (b) vertices, (c) covertices, (d) foci, (e) length of MA, and (f) length…

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Do the three planes x1 + 2x2 + x3 = 4, x2 – x3 = 1, and x1 + 3x2 = 0 have at least one common point…

A: The three planes x1+2x2+x3=4, x2-x3=1, and x1+3x2=0.

Q: Which of the following statements about the finite geometries is/are true ? A. Pappus geometry has…

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Q: Let a = (4, 1) and b = (2, – 2). Find the projection of b onto a. proja

A: We have to find projection of b→ onto a→ for given vectors a→=4,1 and b→=2,-2 We know the projection…

Q: O -L -5) O4-

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Q: In(x + y) dA where R is the triangle with vertices (1,0), (1,1), (0, 1).

A: Let - I=∫∫Rln(x+y)dA Where R is triangle with vertices (1,0),(1,1),(0,1) Equation of line joining…

Q: 10 11 3 vertices at a parallelograni AaCD are shown in the appiet What are the coordinates of point…

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Q: Show whether the sets are connected or not. 1. {z € C | 1< ]z| < 2} 2. D(0, 1) U D(2i, }),

A: 1. Given: D⊂E⊂A then D=E    To Find: To whether the sets are connected.   Where z=x+iy           z…

Q: Discuss the relativr position of the following pair of circles x2+y2-4x-6y-12=0

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Q: 7. Given the points A(-3, -4) and B(2, 0), find the coordinates of the point P on directed line…

A: Here given  endpoint of the line segment Ax1, y1=-3, -4Bx2, y2=2,0 A point P on directed line…

Q: In the 2 dimensional space, which of the following points can not be represented as a convex…

A: We will find out the required values.

Q: Find the coordinates of the point K that lies along the directed line segment from J(4,1) to L(8,11)…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: In the Euclidean 3-dimensional space with a fixed cartesian system, consider the circle C:x +y + z-…

A: The general equation of a circle in 3 dimensional is given by: x-h2+y-k2+z-p2=r2 Here h,k,p is the…

Q: 13. A point lies on the bisector of LABC if and only if it is equidistant fromA and C.

A: To Determine: a point lies on the bisector of angle ∠ABC if it is equidistant from A and C. Given:…

Q: Find the coordinates of point K, so that K partitions the directed segment WQ in the ratio 5:1, if W…

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Q: Find the intersection of the sets. {w, y, z}∩∅

A: Given, w,y,z∩∅we have to find intersection of the sets.

Q: Solve the following problems completely. If there are seven distinct points on a plane with no…

A: Given: Total number of points is, n=7. No three points are collinear. The objective is to find the…

Q: 11. Determine if the statement is true or false. "A kite is a parallelogram"

A: Given the statement, "A kite is a parallelogram"

Q: If there are 7 distinct points on a plane with no three of which are collinear, how many different…

A: A polygon is a closed shape in two dimensional. It do not contain any curves. Thus the minimum…

Q: Given: In a plane, a 1 b, b 1 c, and c || d. Prove: a || d 开! roof

A: We can write the paragraph proof as below.

Q: Find a geometric model for the following axioms, and determine whether or not it is a projective…

A: Yes, it is possible... If you carefully observe, you will see that this should give us a pentagon,…

Q: -4 which of the fillowing sets of points is a eircle whose radius is 5 and whose centre is at the…

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Q: Give another name for Plane N. * D

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Q: If there are 9 distinct points on a plane, no 3 of which are collinear, how many quadrilaterals can…

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Q: Question 7. Let (x,r) topological space and A, BcX. Determine be a whether A-B2A-B or not.

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Q: 1. Let 7 = {1,2). a. Explain graphically the set S = {(x, y) : (x − 3, y − 1) = 0}. b. Draw the the…

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Q: Place three points on the plane such that a vertex of their Voronoi diagram is outside the triangle…

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Q: (a) If C is the line segment connecting the point (x,, y,) to the point (x,, Y½), find the…

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Q: Let a = (- 3, – 5) and b {1, 2). Find the projection of b onto a. proj; b = >

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Q: Find the point O that partitions the directed segment MN in a ratio of 2:3, given the points…

A: The coordinates for the directed line segment MN¯ are M(-3, -2) and N(4, 2) Point O is the point…