Find an equation of a plane passing through the points (1, –3, –59), (–3, 2, 54) and perpendicular to the plane 6x +y+9z+2=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: Obtain the equation of the plane that passes through the points: A (2, 1, -1), B (5, -2, 0), C (0,…

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Q: Find an equation for the plane that contains the line v = (-1, 1, 2) + t(9, 5, 4) and is…

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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 through the point P= (3,3,5) and parallel to the plane y – 5x + 5z =…

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Q: Find the general equation of the plane containing the points P1(-1, 2, 0), P2(3, 4, -1), and P3(-2,…

A: Given points are  P1(-1,2,0)  P2(3,4,-1) and P3(-2,-1,0)

Q: Find the equation of the plane through the point P= (2,4, 5) and parallel to the plane - (5x + 3y +…

A: Parallel plane problem....

Q: Find the distance between the plane P:8x+3y+9%= 0 and the point (1,-5,20)

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Q: Find the equation of the plane through the point P = (2, 5, 4) and parallel to the plane 5x – 5y +…

A: Equation of plane parallel to 5x -5y +3z = 6  is given by; 5x -5y +3z + λ  = 6 Also it passes…

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 the equation of the plane through the point P=(5,2,5) and parallel to the plane 2y−4x−z=9. z=

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Q: Find the equation of the plane pass through two points A(2.1.3) & B(-1,3,-4) & perpendicular to the…

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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 for the plane through P0(-3, 0, 7) perpendicular to n = 5i + 2j - k.

A: given that the plane passes through (-3,0,7) perpendicular to n=5i+2j-k. we need to find the…

Q: Write the equation of the plane that is parallel to the xy-plane and passing through the point…

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Q: Find an equation of the plane that crosses the x-axis at 3, the y-axis at 2, and the z-axis at 5.

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Q: Find an equation for the plane parallel to the liner =1- 21, y = 2 + 3t %3D 2 = 1+ 2t and that…

A: Given: Plane is parallel to the line x=1-2ty=2+3tz=1+2t Also, the plane contains the line of…

Q: Find an equation of the plane that contains the point (2, 0, 3) and the line x =-1+t, y =t, z=-4+21…

A: It is given that the required plane contains the point 2,0,3 and the line x=-1+t,y=t,z=-4+2t. The…

Q: Find the equation of the plane that contains the point (4, 0, −2) and is perpendicular to the planes…

A: The equation of the plane passing through the point x0, y0, z0 is given as…

Q: (b) Find an equation of the plane passing through the point A(0, 9,2) and parallel to the plane 13x…

A: Given that, the given point is A(0,9,2) the parallel line is 13x+2y-z=10. To find the equation of…

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

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

A: This question is based on finding equation of plane when we know 3 points of plane.

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 an equation of the plane containing the point P(1, -2, -2) perpendicular to the line through…

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Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 7z + 13 =…

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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: Find an equation for the plane that passes through the point (1, 3, -5) and is perpendicular to the…

A: Given point is (1,3,-5). The scalar equation of a plane that passes through point (a, b, c) and has…

Q: Find an equation for the plane that passes through the following points. (2, –1, 4), (0, 0, 6), and…

A: Explanation of the solution is given below...

Q: Find an equation of the plane through the origin that is parallel to the plane 4x-3y+5z+13=0

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Q: Find the equation of the plane through the points P (1,-1, 1) Q = (3,–1,3); R= (2,1,1).

A: We will find out the required equation of plane.

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: Write the equation for the plane. The plane through the point P(2, - 2, - 3) and parallel to the…

A: By the using properties we find the required equation of plane.

Q: Find the equation of the plane whose has the line x=2-3t, y=3 + t, z = 5t and passes through the…

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

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Q: Find the equation of the plane which passes through O and is parallel to z –- 3x = -2 %3D х+ y + z =

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

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Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2). O…

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Q: Write the equation for the plane through the points P(-1, 1,-12), Q(2, 8, -49) and R(1, -6, 45). 4x…

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Q: Find the equation of the plane that contains the point A(1, 2,-4) and is perpendicular to 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).

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Q: Find an equation of the plane that contains the point (2,0,-8) and contains the line y- 2 z+1 x +4 =…

A: The plane passes through the point 2, 0, -8. Thus, the equation of the plane can be written as…

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: Find the equation of the plane through the origin that is parallel to the plane 4.r – 2y+ 7z +12 = 0…

A: Consider the general equation of a plane, 4x-2y+7z+12=0 the normal vector of this plane will be…

Q: Find the equation of the plane through Po (2,-1,-1) and P1(1,2,3) and perpendicular to the plane…

A: Given: P0(2,-1,-1) and P1(1,2,3)  2x+3y-5z-6=0

Q: Find the general equation of the plane containing the points P1(0,0,0) P2(1,2,-1), and P3(-1,1,0)

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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.