Describe a method for determining whether four points P, Q , R , and S lie in the same plane?

Q: find aplane through Po (2,!,-1) and perpendicular to the line of Intersectionof the planes 2xty-Z=3)

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Q: Do the points (1, 0,−1), (0, 2, 3), (−2, 1, 1), and (4, 2, 3) lie in the same plane? Justify your…

A: To check: If the points (1, 0,−1), (0, 2, 3), (−2, 1, 1), and (4, 2, 3) lie in the same plane and…

Q: Find a plane through the points (1,-6,1), (-5,-2,3), (-4,5,-4). Write your answer in the form Ax +…

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Q: A snowman with the radius of 4 units and 6 units is standing on the third quadrant of the Cartesian…

A: The given graph is as follows:

Q: Determine whether the statement " If two lines L1 and L2 are each parallel to a plane, then L1 and…

A: Two lines  L1 and L2 can be perpendicular to each other and be parallel to the same plane at the…

Q: Give an example of three planes,exactly two of which are parallel.

A: Give an example of three planes,exactly two of which are parallel.

Q: B. Constructing a parallel through a point (rhombus method) Given: PQ and point K

A: Steps:  1) Place the compasses on point K and set its width to a little more than the distance to…

Q: Explain why it is impossible to find four points on the same plane equidistant from each other.

A: Let us imagine that we have 3 points in a plane that are equidistant from each other. These points…

Q: Suppose that (a) point C lies in plane X and (b) point D lies in plane X. What can you conclude…

A: Let point C and D lies in plane X. A straight line can be formed by joining the points C and D. Let…

Q: Can two horizontal planes intersect?

A: Explanation: If two planes are horizontal, it means both are parallel to the x-axis.

Q: :Find the equation of the plane through (-1 6, 2) and perpendi cular to the jain of (1, 2, 3) and…

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Q: 2) Calculate the distonce d of the pint ? (-l,(, -2) from the plane passing through the three A(…

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Q: Plot the points (−3, 2), (4, −2), (3, 1), (0, −2), and (−1, −2) in the Cartesian Plane.

A: To plot the points (−3, 2), (4, −2), (3, 1), (0, −2), and (−1, −2) in the Cartesian Plane. Given…

Q: Determine whether the points are coplanar.(0, 0, −1), (0, −1, 0), (1, 1, 0), (2, 1, 2)

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Q: ectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,-4), R(6,-2,-5), and is…

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Q: 2. The x- and y-axes divide the coordinate plane into four regions called

A: Given: The x and y axes divide the coordinate plane into four regions

Q: In Cartesian space, the point (0,6,0) lies 6 units above the origin. Select one: True False

A: We have to find the point location

Q: Find the areas of the parallelograms whose vertices are given in Exercises 35–40. 35. A(1, 0), B(0,…

A: Area of parallelogram ABCD is |AB x AD|

Q: A power cable is to be fitted under a road and can be represented on 3D Cartesian axes as below,…

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Q: Determine homogeneous coordinates of the points (3,4) and (1-,7)

A: Homogeneous coordinate:-converting any two dimension coordinate to three dimensional coordinate  (x,…

Q: Name three points that determine plane M.

A: Given, two planes M and N that intersect on line passes through A and B in image we can see three…

Q: Choose two figures which are topologically equivalent to each other

A: Two figures are said to be tropologically equivalent if they can be tranformed into each other…

Q: the coordinate plane be

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Q: plot the given pair on a cartesian plane {(1,1),(2,4),(3,7),(4,10),(5,13)}

A: The given pair of points are  A(1,1), B(2,4), C(3,7), D(4,10), E(5,13)

Q: prove that points are collinear 3. P(-15,10), Q(0,-20), R(-10,0)

A: Given ; The points are P(-15,10), Q(0,-20), R(-10,0) .

Q: Plot the points (5, 5), (−2, 0), (−3, 6), (−1, −7) in the Cartesian Plane.

A: A point x,y on the cartesian plane represents that the distance of the point from y-axis is x and…

Q: Write the characterisation of two parallel planes (given in general forms) in terms of the cross…

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Q: Do three points determine a plane?

A: We know by following ways plane can be determined: 1. Three non collinear points determine the…

Q: 5. Find the dimension of the largest rectangular building that can be placed on a right-triangular…

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Q: Which of the points A(-4,0,–1), B(3,1,–5), and C(2,4, 6) is closest to the yz-plan Which point lies…

A: Given: A(-4,0,-1)  B(3,1,-5)  and C(2,4,6) To find: Which is closet to the yz plane Which is lies on…

Q: 2) Do the points (1,0, -1), (0,2,3), (-2,1,1), and (4,2,3) lie in the same plane?

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Q: 3) Find the plane through the points: A(2, 4, 5), B(1, 5, 7) and C(-1, 6, 8)?

A: Let the given points are:

Q: 3. What are the three possibilities for the intersection of a line and a plane?

A: The solution is given in the next step.

Q: Name the intersection of planes M and N.

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Q: If two planes intersect, is it guaranteed that the method of setting one of the variables equal to…

A: Let say one the intersecting two planes is Ax + By + Cz =D When we put z = 0 the Plane reduces to…

Q: Represent two planes that intersect at a line represented by 3 +2

A: There are so many pair of planes that represents the same line.

Q: *15. What is the name for the point on the coordinate plane that has the (Inv. 7) coordinates (0,…

A: The given point is: (0, 0)

Q: Determine whether the four points P:(1, 1, 2), P:(4, 0, 3), P:(1, 5, 10), and P.(7, 2, 4) lie in the…

A: 4 points are given and we have to check whether these lie in same plane or not.

Q: use set theoretic or vector notation or both to describe the points that lie in the given…

A: Consider the parallelepiped in three dimension. let us consider,  a=AB→b=AD→c=AC→ For an arbitrary…

Q: Do two points determine a plane?

A: No.

Q: Find the distance from the point (-2, 1, 4) to the plane x = 3

A: Given: The point -2,1,4 and plane x=3 To find: Distance from the given point to the given plane.

Q: Describe a method for determining whether four points P , Q , R , and S , lie in the same plane

A: We know that if some points lie on the same plane, then their slope would be same.

Q: Find an equation of the plane through the three points given: P = (0,0, 2), Q = (-4, 1, –1), R = (2,…

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Q: Determine whether the three points P = (8,-2,-6), Q = (11, 4, 3), R = (14, 12, 12) are collinear by…

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Q: Show whether or not the diagonals of parallelogram ABCD bisect each other given A(-2,2), B(1,4),…

A: The vertices of the parallelogram are given  A(-2, 2) B(1, 4) C(2, 8) D(-1, 6)

Q: Find an equation of the plane through the three points given: P=(0,0,3), Q=(2,−3,2), R=(−1,1,0)

A: find the equation of the plane

Q: Do two distinct lines in space determine a unique plane? Explain.

A: Yes ,  two distinct lines in space determine a unique plane

Q: Write a description of some model of Lobachevskian geometry. Specify the "plane surface" and what…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.