Determine if the two planes 6x + 18y + 14z =-2 and the plane containing the points (1, -1,9), (4, -1, 2) and (-2,3, 4) are parallel, orthogonal or neither.

Q: Determine an equation for the unique plane that passes through the points P(0,0, 2), Q(0,4, 0), and…

A: Given points are P(0,0,2), Q(0,4,0) and R(8,0,0). Find an equation for the unique plane that passes…

Q: Find the equation of the plane passing through the points P1 (1, 2, ─1), P2 (2, 3, 1) and P3 (3,…

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Q: 3. Find the Scalar eguation of the plane containing the line rt) =<!,2,-37+ -3,2, 17 and the point…

A: Given problem:- Find the scalar equation plane containing the line  r (t)= &lt;1,2,-3 &gt; + t &lt;…

Q: Find the point at which the line (3, 4, 5) +t(1, -1, –5) intersects the plane -5x + 2y+ z = -86.

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Q: Find the standard equation of the plane that contains three points A(1,0,–1), В(2, 1, 1) and C(1, 2,…

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Q: Find an equation of the plane that passes through (2, –1, 5) and is parallel to the plane containing…

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Q: Find a plane through the points P(4,-1,2), Q(6,2,1) and perpendicular to the plane -x+y+z=3

A: Given: Points, P(4, -1, 2) Q(6, 2, 1)

Q: (b). Determine the equation of the plane that contains the points P(1, –2,0), Q(3, 1, 4) and R(0, 1,…

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Q: Determine if the two planes 6x + 18y + 14z = -2 and the plane containing the points (1, –1,9), (4,…

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Q: Find an equation of the plane determined by the points P(0,0,0), Q(-1,2,4), and R(2,1,3)

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Q: Find an equation of the plane. The plane that passes through the point (−1, 3, 2) and contains the…

A: given planes are x+y-z = 5, 4x-y+5z = 1 The equation of plane that contains intersection of planes…

Q: Find an equation of the plane that contains all the points that are equidistant from the given…

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Q: Find an equation of the plane passing through (0,-2,3) that is orthogonal to the planes 2x+ 2y-5z 0…

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Q: Find the equation of the plane through (3,2,1) and (3,1,-5) and is perpendi čular to the plane 6x+…

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Q: Find an equation of the plane containing the three points P(1,2,2), Q(2,-1,4), and R(3,5,-2).

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Q: Find an equation of the plane consisting of all points that are equidistant from (1, 0, -2) and (3,…

A: Let's assume the coordinates of all the points which are equidistant from a points (1,0,-2) and…

Q: Find an equation for the plane containing the three points (0, 1, -1), (1,0,1), and (2, 1, 0). Where…

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Q: Find an equation of the plane. The plane that passes through the point (−2, 3, 2) and contains the…

A: This question can be solved using the concept of planes in three dimensional geometry.

Q: Find an equation of the plane consisting of all points that are equidistant from (2, 4, 2) and (-2,…

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Q: Find a plane containing the point (1, 3, 3) and the line of intersection of the planes - 2x - 3y -…

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Q: Find the equation of a plane consisting of all points that are equidistant from (5,5,-1) and…

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Q: Determine if the three planes -x-5y-5z= 2, 4x -5y +4z = 19 and x +5y - z = - 20 have an intersection…

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Q: Determine the equation of the plane that contains the points P(1,−2,0), Q(3,1,4) and R(0,1, -2)

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Q: Find an equation of the plane that contains all the points that are equidistant from the given…

A: Let the point P(x,y,z) be on the required plane which is equidistant from the given points (1, 0, 2)…

Q: Determine the equation of the plane containing the points: P (1, 2, -3), Q (2, 3, 1) and R (0, -2,…

A: Vector equation of a plane passing through three points with position vector P→,Q→,R→is given by…

Q: Find an equation of the plane passing through (0,-1,3) that is orthogonal to the planes 3x+4y-2z=0…

A: Let's find equation of the plane.

Q: Find an equation of the plane passing through P = (1, 2, 3), Q = (0, 0, 3), and R = (−2, 5, 4).

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Q: Find the equation of the plane passing through (2, 0, 1) and (-1, 2, 0) and perpendicular to the…

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Q: 5) Determine whether the plane 3x – 4y + 5z = 0 and the plane - 6x + 8y – 10z - 4 = 0 are in…

A: We find out the results by using vectors in 3D

Q: 2. Find an equation of the plane determined by the points P(1,1,0), Q(1,0,1) and R(0, 1, 1).

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Q: Find the equation of the plane that passes through the points A = (1, –4, –1), В - (-5, —3, —5), and…

A: Proceed as shown below

Q: 8. Determine if point A(-1, -3, 9) lies on the plane T: 8x-3y+2z=4

A: The point lies on the plane if the coordinates of the point satisfy the equation of the plane.

Q: Find an equation of the plane consisting of all points that are equidistant from (-2, -1, 0) and (0,…

A: Find an equation of the plane consisting of all points that are equidistant from (-2, -1, 0) and (0,…

Q: Find an equation for the plane consisting of all points that are equidistant from the points (-6, 3,…

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Q: Find an equation of a plane containing the three points (2, 0, 5), (6, 2, 8), (6, 3, 10) in which…

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Q: Determine if the two planes 6x + 18y + 14z = -2 and the plane containing the points (1, –1,9), (4,…

A: First we have to find Normal vector of both planes.

Q: Find the equation of the plane containing the points (0, 1, 3), (2, 2, 2) and (3, 2, 1)

A: Given: points (0,1,3), (2,2,2), (3,2,1) Find: equation of the plane containing given points

Q: Find an equation for the plane through the points (-2, –2, 0),(-1,4,–9), and (–10, –6, –4). tion for…

A: Given points are -2,-2,0 -1,4,-9 and -10,-6,-4find the equation of a plane

Q: Find an equation of the plane. The plane that passes through the point (−3, 2, 1) and contains the…

A: It is known that equation of a plane passing through line of intersectionof planes .…

Q: Find a plane containing the point (5,8,8) and the line of intersection of the planes -4x 4y+ 6z = 74…

A: We have to find the equation of plane containing the points 5,8,8 and the line of intersection of…

Q: Determine the equation of the plane that contains the points P=(1,-2,0) P=(1,-2,0), Q=(3,1,4)…

A: Here we have to determine the equation of the plane that contains the points P(1,-2,0), Q(3,1,4) and…

Q: Determine the general form of the equation of the plane passing through P(2,1,-1), Q(0,-2,0) and…

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Q: Find the equation of the plane containing the points P = (−1, 1, 0), Q = (3,2,4) and R = (4,3,1

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Q: Determine an equation for the plane that passes through the point (1, 2, –3) and is parallel to the…

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Q: Question 10

A: We have to find equation of plane that is parallel to the plane 6x-5y+8z+18 =0 and  the pale passes…

Q: Find an equation of the plane consisting of all points that are equidistant from (-1, 3, 2) and (2,…

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Q: What is the equation of the plane containing the points (4,−3,1), (−3,−1,1) and (4,−2,8)? A. 14x…

A: Solve by eq

Q: 3) Find an equation of the plane which contains the points P(-1,2,1), Q(1, –2, 1) and R(1,1, –1).

A: Equation of a plane passing through 3 points P(x1,y1), Q(x2,y2) and R(x3,y3) is given by,…

Q: 4. Determine the general equation of the plane containing the points P(1, -4, –5), Q(2,0, 13) and R

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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.