Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane whose general equation is 2x + 3y -z = 0.

Q: Find an equation of the plane that is parallel to the plane x + 8y – 4z + 12 = 0 and contains the…

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

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Q: Find the equation of the plane containing the line of intersection of the two planes z+y+z+5=0 and…

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Q: Find the distance from the point (3, 2, 5) to the plane whose general equation is 2x + 3y - z = 0.

A: we have to find the distance from the point (3,2,5) to the plane whose general equation is 2x+3y-z=0…

Q: Find an equation for the plane in R³ spanned by the points (1,5,

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Q: Find an equation of the plane that is parallel to the plane x + 2y – 4z + 16 = 0 and contains the…

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Q: Determine an equation of the plane that contains the point (1, 1, 2) and is parallel to the plane…

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Q: Find an equation of the plane that is parallel to the plane x + 4y – 3z + 16 = 0 and contains the…

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Q: Find an equation for the plane passing through the point P(-2, 1, 1) and parallel to the plane 3x +…

A: Solve for the equation

Q: Find the distance from the point (-1, 3, -1) to the plane -1x + 2y -5z=1.

A: Given: The point (-1, 3, -1) and the plane -1x+2y-5z=1 To find: The distance.

Q: Find the equation of the plane containing the point (- 7, – 8, 0) and parallel to the plane 6x + 8y…

A: To find equation of a plane we use Concept of Direction Ratio of the given parallel plane.

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

A: The parametric equations of the line x=3y=4z may be re-written as  so that its vector equation is…

Q: Find the distance between the point (-1, 1,-1) and the plane 3x - 5y + 2z = 12

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Q: Find the equation of the plane through the point (1,2,-1) and parallel to the plane 2x- 3y+4z+6-D0.…

A: To find: The equation of plane passing through the point 1,2,-1 and parallel to plane 2x-3y+4z+6=0.…

Q: find the equation of the plane passing through(1,0,-1)&(-1,2,1) and parallel to the line of…

A: To determine: The equation of the plane passing through the points (1, 0, -1) and (-1, 2, 1) and…

Q: The equation of plane through the origin and parallel to the plane 2x+ 5y – 4z = 8 is 2x + 5y – 4z =…

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

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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 of the plane. The plane through the point (5, –1, –6) and parallel to the plane 5x…

A: Given point is (5,-1,-6) and plane is 5x-y-z=3 find the equation of the plane which is parallel to…

Q: 4. Give the general equation of the plane containing the point (3,-1,4) and 2- z perpendicular to…

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Q: Find an equation of the plane through the given point and parallel to the given plane. origin 2x -…

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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 an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: Find an scalar equation of the plane containing the line x = 2 – 4t, y = 4 – 5t and z = 5+t and the…

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Q: What is the equation of the plane parallel to 3x + 4y − z = 5 passing through the origin?

A: 3x+4y-z=5

Q: Determine the Cartesian equation of a plane that passes through a point (2,1,-5) and perpendicular…

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Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: Find the general form of the equation of the plane with the given characteristics. Passes through…

A: The plane, let P1, whose equation is required is perpendicular to the plane, And passes through the…

Q: Find the equation of a plane that passes through the point (0,0,0) and contains the line x = 2 -t y…

A: Here we have to find the equation of a plane that passes through the point (0,0,0) and contains the…

Q: Find the scalar equation of the plane that contains the line x+1 -3=. and is parallel to x+2=+4_:+2…

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Q: The equation of plane through the origin and parallel to the plane 2x +5y-4z = 8 is 2x + 5y- 4z = 0.

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Q: Find the equation of a plane that passes through the origin and contains the line x = 2t, y = 3t, z…

A: Consider the provided question, The equation of a plane passing through the point (x1, y1, z1) is…

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

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Q: Find the distance between the point (2, 0, 1) and the plane 2x - 3y + 6z = 6.

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Q: Find the equation of the plane containing the point (4, -1, 3) that is parallel to the plane 2x - 3y…

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

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Q: Find an equation of the plane. The plane through the point  (3, −4, −7)  and parallel to the plane…

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Q: Find the equation of a plane through the point (3, -2, 8) and parallel to the plane z=x+ y.

A: Given, Plane is passing through the point (3, -2, 8) and Parallel to the plane z=x+y    Equation of…

Q: Find an equation of the plane passing through (0,−3,1) that is orthogonal to the planes 5x+5y−4z=0…

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Q: Find an equation of the plane that passes through the point (1,2,3) and which is orthogonal to the…

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Q: Find an equation of the plane. The plane through the point  (8, −3, −3)  and parallel to the plane…

A: We know that two parallel planes have same direction ratios(i.e. the coefficients of x,y and z…

Q: 4. Determine the equation of the plane passing through the point (1, -4, 3) and parallel to the…

A: We have to find an equation of the plane passing through the point (1, -4, 3) and parallel to the…

Q: Find the equation of a plane through the point (3, -2, 8) and parallel to the plane z = x+ y. Leave…

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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: Find an equation of the plane. The plane through the point (7, −2, −7) and parallel to the plane 9x…

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Q: Find an equation of the plane. The plane through the point (7, –2, –8) and parallel to the plane 6x…

A: We will solve the following.

Q: 3. Find the equation of the plane parallel to the plane with equation 18x + 6y – 5z = 0 and passing…

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Q: perpendicular

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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.