Consider three points in three-dimensional space: ?=(11,2,−3),?=(2,−3,11),?=(−3,11,2) Let ? be the plane which is perpendicular to ??→ and the point ? lies on plane ?.  Find the equation for the plane ? written in the form: ??+??+??+?=0

Q: Determine a cartesian equation of the plane through the points  P1 =(1,2,-1), P2=(0,2,-3) and…

A: Determine a cartesian equation of the plane through the points  P1 (1,2,-1), P2(0,2,-3) and parallel…

Q: Find the Cartesian equation of the plane containing the point P(1,3,-2) and the I T = (0, -1, 4) +…

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Q: find an equation for the plane through pointsP, Q, and R. P(1, -1, 2), Q(2, 1, 3), R(-1, 2, -1)

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Q: Find the equation of the plane parallel to the intersecting lines (1,2 +t, -3 – 3t) and (1 – t, 2 –…

A: Let, the direction vector of 1,2+t,-3-3t is v1=0,1,-3 and the direction vector of 1-t,2-3t,-3-2t is…

Q: A plane in space contains the three points (2,1,3), (1,1,4) and (2,-1,3). Which of the following is…

A: Given points are (2,1,3) , (1,1,4) and (2,-1,3)

Q: 4. Consider the points A(1, 0, 3), B(-1, 5, 2) and C(3, -1, 1). Find the equation of the plane…

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Q: Consider the points P = (2,-1,4), Q=(1,1,1), and R=(3,1,-2) in xyz-space. An equation of the plane…

A: Solution is given bellow

Q: Find an equation of the plane containing the points A = (1,0,2), B= (– 1,1,2),C=(5,0,3).

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Q: Let A be the plane containing the points P(2,2,2), Q(2, 1,3 ) and R(3,1, 3) . (a) Find the equation…

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Q: M (1; -2; 4) parallel to the OXZ plane

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Q: You are given the following points: A = (11, –14, –16), B = (16,0, 5), C = (-9, 16, 13). Which point…

A: Answer

Q: Which of the following is the equation of a plane parallel to the yz-coordinate plane and passing…

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Q: a)What is the distance between the point A(3,1,-1) and the plane 4x + 4y +7z +2=0 ? b) Find the…

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Q: Find the Cartesian equation of the plane containing the points A(1,0,3), B(1,1,-2) and C(-1,2,0).…

A: Solution

Q: Which of the following points is on the xy and yz planes, but is not on the xz plane? a) (2, 0, 0)…

A: We can represent 3D coordinate system.

Q: Perpendicular to i = 2ỉ - 33 + 5k and through (4, 5, –2).

A: Here is the solution of the given problem. Co-ordinate Geometry 3D - Plane.

Q: Find the Cartesian equation of the plane containing the points A(4,0,4), B(1,5.5) and C(-1,-1.2).…

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Q: Find the equation of the plane with the given description. Passes through P = (3, 5, −9) and is…

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Q: 1. Find the equation of the plane that contains the line point (1,3, 2). 무 =D북3부 md the

A: Let's find.

Q: Let P = (-2,0, 5), Q = (3, 1, 1), and R = (0,0, 4) and define a = PÓ and b= PR. Find (d) The…

A: Given three points are: P:-2,0,5, Q:3,1,1, R:0,0,4 The position vectors for the given points are:…

Q: Find the Cartesian equation of the plane containing the points A(- 1,0, 1), B(2, 1, 3), C(4, – 2,…

A: topic - equation of plane through three points

Q: Consider the points: A = (1,0,0), B = (2,3,5) and C = (-0, –3, –1). The equation of plane which…

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Q: Consider the points: A = (1, 0, 0), B = (2, 3, 5) and C = (-4, –4, –2). The equation of plane which…

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Q: Q3// :- Write an equation for the plane containing points P=(1,1,-2),Q=(0,2,1), and R=(-1,-1,0)

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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: Determine the equation of the plane that contains the points P_0 = (1, 0, 0), P_1 = (0, 1, 0) and…

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Q: Find the standard equation of the plane that contains three points A(1,0,-1) B(2,1,1) and C(1,2,-3).

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

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Q: Which of the following is the equation of the plane containing the points (2,1,2), (4,1,0) and (5,0,…

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Q: Write an equation for the plane that contains the x-axis and the point (0, 8, 24). O 3 = x² + y? +…

A: Please refer the attached image for complete solution.

Q: Find the equation of the plane which contains the line ( 2 + t , 3 − t , 4 + 2 t )and the point ( 0…

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Q: Find an equation for the plane containing the three points P = (1, 2, 3), Q = (3, 1, 2), and R = (2,…

A: To find an equation for the plane containing the three points P = (1, 2, 3), Q = (3, 1, 2), and R =…

Q: Find the equation of the plane for all points equidistant to (1, -1, 1) and (0, -5, -2).

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Q: Find an equation of the plane each of whose points is equidistant to the point H(4, 2, 5) and to the…

A: Basic 3D Geometry problem

Q: Find the equation of the plane that contains the line r¡(t) = (1 + lt, –1+t, 2+ 8t) and the point…

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Q: Which of the following are equations for the plane through thepoints P(1, 1, -1), Q(3, 0, 2), and…

A: The points P1,1,-1,Q3,0,2, and R-2,1,0. We have to find the equation for the plane through these…

Q: Write an equation for the plane that contains the x-axis and the point (0, 5, 10). O z = 5x + 10y O…

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

A: Let plane contain point x,y,z.

Q: The general equation of the plane that containsteh points (1,0,3),(-1,1,-3)and the origin is of the…

A: Given general equation of plane is

Q: Find the Cartesian equation of the plane containing the points A(1,0,3), B(1,1,-2) and C(-1,2,0).

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Q: Write an equation for the plane that contains the x-axis and the point (0, 5, 15). O 3 = x² + y² +…

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

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

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Q: -. Which coordinate plane is closest to the point (7, 3, 8)? Find an equation of the sphere with…

A: we have to find the coordinate plane that is closest to the point 7,3,8 and also find the equation…

Q: The general equation of the plane that contains the points (1, 0, 3), (-1,1,-3), and the origin is…

A: Explanation: Given that,  equation of plane ax+by+cz=0and (1,0,3), (-1,1,-3) and (0,0,0) on the…

Q: EK does not appear to be parallel to the plane containing which points? d. Q. S, C а. U. A. С b. Q.…

A: Parallel lines are two or more lines that lie in the same plane and never intersect. To show that…

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.