1) Consider the two planes x 2y + z = -5 and 3x 2y - z = 1 (a) Find an equation for the line of intersection between the two planes. (b) Find an equation for a plane that is orthogonal to both planes and passes through the point (2, 3, -1).

Q: 11) Find the equation of the plane that passes through the point (1, 5, 1) and is perpendicular to…

A: A plane is passing through a point (1,5,1) and is perpendicular to the planes 2x + y - 2z = 2 and x+…

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 an equation for the plane through the point (0, –4, 5) which is perpendicular to the line…

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

A:

Q: 1 Find equation of plane which is containing Points A(2,1,1) and B(7,5,2) and normal to 2 x - 3y -…

A: We have to find the required plane

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

A:

Q: Find the equation of the plane passing through the point (-1, 4, 0) perpendicular to the line L₁: x=…

A:

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

A: Given: Equation of planes x+y-z=5⇒x+y-z-5=0 and 3x-y+5z=3⇒3x-y+5z-3=0 and point -1,2,2, To find: The…

Q: Find parametric equations for the line of intersection of the planes x + 2y + 3z = 4 and 5x + 6y +…

A: Given: x+2y+3z=4   and  5x+6y+7z=8To obtain the parrametric…

Q: Find the intersection between the plane  4x−y+5z=18  and the line through the points  (0,0,1)  and…

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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 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 the general equation of the plane spanned by

A: Given vectors are 111 and 321

Q: What is the equation of the plane through (-1,-1,-1) parallel to the plane x+ 2y + 3z = 9?

A: The vector normal to the plane ax+by+cz=d is ai^+bj^+ck^ . The plane parallel to this plane has the…

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

A:

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

A:

Q: Consider the planes of equations −y+z−2=0 and x−y=0. a) Show that the planes intersect. b) Find…

A: We can solve this using definition of intersection of plane

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 an equation of the plane containing (1, 5, -1) that is perpendicular to the line of…

A:

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

A: Using Distance from point to plane formula,

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

A:

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

A: Given problem:- Determine the general equation of the plane π passing through the point P(1, -4,-5)…

Q: 37 Find the equaton of a plane that contains the point (4, -3, –1) and is perpendicular to the…

A:

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

A: Please see the explanation below

Q: Find an equation of the plane that is parallel to the y-z plane and that passes through the point…

A: NOTE: Refresh your page if you can't see any equations. . the equation of any plane parallel to 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: Find an equation of a plane passing through the points (1, –1, 7), (3, 2, –20) and perpendicular to…

A:

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

A:

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

A:

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

A:

Q: Find an equation of the plane in standard form (ax + by + cz = d) that passes through the point (4,…

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Q: 6) Find the distance between the point (1, -4, -3) and the plane 2x – 3y + 6z = - 1.

A:

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

A:

Q: Give the general equation of the plane satisfying the given condition. plane Σ containing the point…

A: We will find the equation of the plane Σ which is parallel to the plain 2x − 6y + 3z = 0 and…

Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is

A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.

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

A:

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

A:

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: The intersection point of the line that passes through the origin and is perpendicular to the plane…

A:

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: 4. What is the equation of the plane through (-1,-1,0) parallel to the plane x + 2y + 3z = 9? (a) x…

A: To find the equation of the plane through (-1,-1,0) parallel to the plane x+2y+3z=9

Q: Find an equation of the plane perpendicular to each of the planes z – y+z = 0 and 2r+y-4z–5 =0 and…

A: The given problem is to find the equation of plane perpendicular to each of the given planes and…

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

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Q: Find the intersection of the plane 3x – y + 2z – 3= 0 and the line

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

A:

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

A: To find the distance

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.