(a) Describe the 3 dimensional shape determined by the equation below. 12 - 2r – 26 + y² + 4y + 2² – 6z = 0 (b) Which of the points (if any) P(3, 4, 1), Q(-2, 3, -1), and R(2, 3, -1) lie on the plane 2(r – 2) +3(y – 2) – (z + 4) = 0?

Q: equation of the plane that passes through the point (1.4.2) and contains the line of the…

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Q: 4 The plane t contains the point P(-1,2, -4) and the line 4:r=(2i-5j-3k)+1(-4ị +2j+k) (a) Show that…

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Q: The equation of the plane that contains the three points (1, 2, 0), (1, 3, 1), and (3, 0, 4) is 6x…

A: Cartesian equation of a plane passing through three non collinear points A(x1,y1,z1), B(x2,y2,z2),…

Q: (b) Find the equation of the plane passing through the points A(2,2,1), B(9,3,6) and perpendicular…

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Q: 19. 19. Find an equation of the plane that passes through the points (3.0. 1). (2. 2.3). (7,1, 4). 점…

A: The plane is passing through the points (3, 0,-1) , (-2, -2, 3) and (7, 1, -4)

Q: An equation of the plane passing though the points A(-1;2;0),B(0;1;2) and C(1; -1;0) is: O…

A: It is know that equation of plane passing through points x1,y1,z1,x2,y2,z2 and x3,y3,z3 is…

Q: 7. a) Find the equation of the plane passes through the point P(1,2,-1), perpendicular to…

A: We have to solve given problems:

Q: (vi) Find an equation of the plane that passes through the line of intersection of the planes x – z…

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Q: 4 The plane t contains the point P(-1,2,–4) and the line 14:r=(2i-5j-3k)+1(-4ị + 2 j+k) (a) Show…

A: Since you have asked multiple subparts, as per our company guidelines we are supposed to answer only…

Q: 4. Find the general equation of the plane passes through the points (3,2,1) and (3,1,–5), and is…

A: We have to find the plane equation

Q: Example 8: Find the point where the line 2t, and z = -3t intersects the plane x = 1 + t, y = –…

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Q: The Cartesian equations of the line perpendicular to the plane 2x -3y + 4z + 8=0 and passing:…

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Q: Example 8: Find the point where the line x = 1 + t, y = 2t, and z= -3t intersects the plane…

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Q: 2.) ( the plane 2x-3y+z =6, and is parallel to the line of intersection of the planes x-2y+z=4 and…

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Q: ....... Q4): A: Find the equation of the plane passing through p(2,-1,-1) and Q(1,2,3) and…

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Q: Find an equation of the plane that passes through the point (-1, 4, 2) and contains the line of the…

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Q: The equation of the plane passing through A(2,1, – 1), B (0, –2,0), and C(1,-1,2) is: O 2x+y-z=0…

A: solve the following

Q: 19. Find the Cartesian equation of the plane a) passes through point A(6,- 7, 4) and parallel to the…

A: To find the Cartesian equation of the plane, a)Which passes through the point A6,-7,4 and parallel…

Q: 0/ Find the Palametric equations of the line of intersection of Planes? PL= -2x+3y +7Z =-2…

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Q: Q1: Formulate the equation of plane in space that contain two points (2,4,-1) and (1,3,-2) and…

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Q: Determine the general equation of the plane 2 passing through the point P (1, -4, -5) and parallel…

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Q: 6x2 - 4xy + 6y2 + 16z2 - 33 = O 6 -2 -2 A = 16 Find the equation of the rotated quadratic surface in…

A: For the equation ax2+by2+cz2+2f yz+2g zx++2hxy, the matrix is ahghbfgfc

Q: C-9: The reflection of the plane 2x-3y+4z-3 = 0 in the plane x- y+z-3=0 is the plane.

A: Topic:- reflection of a plane in another plane.

Q: Q2] [3M] Find the equation of the plane passing through the points P(1, 0, 2), Q(2, 1, 0) and R(2,…

A: As per the guidelines, we are supposed to answer one question only. I am answering the first…

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

A: We have, Vectors in the plane are, Therefore, equation of plane passes through 3 points will be,…

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

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Q: 1. Find the distance between the two planes - 2y + z=4 and z-2y+ :-1 HI

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Q: 6) Consider the plane P : x+y – z = 0 in R³ that contains both the points P(1,0, 1) and P2(0, 1, 1).…

A: • In the first part, we have to use the general Cartesian equation of a line passing through two…

Q: c) Find an equation for the plane parallel to the plane 2x – y + 2z = -4 if the point (3, 2, –1) is…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: -1. Find an equation for the plane consisting of all points that are equidistant from the points (1,…

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Q: 3. Find the equation of the plane containing both the point (1, 2, 3) and the line r(t) = (t, 2t+1,…

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Q: The z-coordinate of the point of intersection of the plane r+2y +z= 6 and the line through the…

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Q: All points x, y) in the plane equidistant from (1,7) and (-1,5) satisfy which of the following…

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2) and…

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Q: 4 /5 . 135% + - (a) Find parametric equations for the line of intersection of the planes x+2y- = 3…

A: In X plane, put y=z=0 & in Y plane put x=z=0 &in Z plane put x=y=0

Q: 13. Consider the point P(3,2,1) and the plane given by the equation 3x +2y+z=0 on the plane closest…

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Q: 24. Find the intersection of the planes x-y-9z = 86 and -4x + 6y + 7z =-87 [Ans: x = 3 - 49t y =-2 +…

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Q: II. Find an equation of the plane containing the points (0,2,-1) and (1,-1,-1) and perpendicular to…

A: we have to find the equation of plane.  Let, a,b c are the direction ratios of required plane 1.

Q: Find an equation of the plane containing the point (3,0.-4) and perpendicular to the line r(t)=…

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Q: - Find the equation of the plane that passes through the three points A(1,0,0), B(0,2,0), and C(0,0,…

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Q: The equation of the plane passing through A(2,1,-1), B(0,–2,0), and C(1,-1,2) is: None of these O…

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Q: 20. The Cartesian equation of the plane which contains the point (1, -2, 3) and perpendicular to x-7…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: äi 8 Find an equation of the plane that passes through the point (-1, 4, 2) and contains the line of…

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Q: 16. Find an equation of the plane through the point (1, 1, –2) and parallel to the plane 3r – z =

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Q: H.W 8- Find equations of the planes that are parallel to the plane x +2y- 2z= 1 and two units away…

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Q: An equation of the plane passing through the points A(-1;2; 0),B(0;1;2) and C(1; –1;0) is: O…

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Q: Q: find the cartesian equation of the plane Containing the point p(2.1.1) and parallel to the plane…

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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.