Question: By using normals, analyze the geometric relationship of the systems of equations. Determine the intersection of the planes, if it exists. If the intersection is a line, express your answer in parametric form.  a) P₁ : 2x + y + z = 6      P₂ : x - y - z = -9     P₃ : 3x + y = 2 [One POI (-1,5,3)] b) P₁ : 2x - y + 2z = 2      P₂ : 3x + y - z = 1      P₃ : x - 3y + 5z = 4 [Show Co-planar-Triangular Prism] c) P₁ : 2x + y - z = 0     P₂ : x - 2y + 3z = 0     P₃ : 9x + 2y = 0 [Intersects at Line-State Line]

Q: The type of coordinate system that allows you to locate any point in space by using X, Y and Z…

A: The type of coordinate system that allows you to locate any point in Space by using X ,Y and Z…

Q: The given points are (4,2,2), (2,6,2) and (0,2,6). Find the general equation of the plane. Solve in…

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Q: Date Directions: Write an equation passing through the point and PARA 1. (4, 7); y = 3.r +,6 m=3…

A: We need to find equation of line passing through given points and is parallel.

Q: Explain how to tell when two planes are perpendicular.

A: Consider two planes. A1x+B1y+C1z=D1 and A2x+B2y+C2z=D2. Here A1,A2,B1,B2,C1 and C2 are direction…

Q: A city is described parametrically by the equation r = (ai + bj+ck) + svi + tv₂ where v₁ = 3i+j+ k…

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Q: 6. The z-axis. Answer:

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Q: Write down the equation of the plane containing the point (-8, 3, 7) and parallel to the plane given…

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Q: Determine whether the graph of the given equation is symmetric with respect to the x-axis, the…

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Q: (x + 4)2. (v- 1)² 1? 36 What are the lengths of the major and minor axes of 16 A Major: 36; Minor:…

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Q: Find the distance from (-5,9, –12) to each of the following: 1. The xy-plane. Answer:

A: Given point :-  (-5,9,-12) To find:- Distance of given point to plane xy

Q: Find the distance from (-5, 9, -12) to each of the following: 1. The xy-plane. Answer: 2. The…

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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: Determine whether the two planes x-y + 2z = 1 -x-y +z = 3 are parallel or intersecting. Find their…

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Q: When the coordinates of two points are (x , y ) and (x, -y) what line symmetry do the points share?…

A: We know for two points,  i) (x, y) and (x, - y) has x axis as line of symmetry.  ii) (x, y) and (-…

Q: Determine the parametric and symmetric equations for the line through the given points (2, –7,5),…

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Q: Find the equation of the line that...is parallel to 7x + 2y = 2 and passes through (3,4). (Write…

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Q: Do two points determine a plane?

A: No.

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.