Find the point on the plane −2 x+y−z =−9 that is closest to the point (3,−2,2) .

Q: 3,0 on a coordinate plane

A: we have to plot (3,0) on a coordinate plane using graph we can plot (3,0) on coordinate plane as…

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

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Q: Find an equation of the plane. The plane that passes through the point (-3, 1, 2) and contains the…

A: This question is related to planes. We will solve this question by using property of plane

Q: Find distance from point (-6, 3, 5) to the plane – 2y – 4z = 8| -

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Q: Find the angles between the planes x + y = 1, 2x + y - 2z = 2

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Q: Solve for the distance from the point (-5, 4, 5) to the plane −x+4y−5z=4.

A: Given Plane: -x+4y-5z=4 and Point: (-5,4,5)

Q: Find an equation of the plane that passes through the points (-2, 1, 1), (0, 6, 11), and (1,0,-1).…

A: We need to find the equation of the plane that passes through the points - (-2,1,1) , (0,6,11), and…

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

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Q: Find an equation of the plane that passes through the points (-6, 1, 1), (0, 4, 7), and (1,0, –1).…

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Q: Find an equation of the plane. The plane through the point (8, -8, -8) and parallel to the plane 5x…

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Q: Find symmetric equations for the line of intersection of the planes. 2 3x - y - 7, 2- Sx + 2y - 8 O…

A: Given:- Planes 1 z= 3x-y-z-7 Plane 2 z=5x+2y-8 To find:- Find symmetric equations for the line of…

Q: Find the point at which the line (-3, 4, 2) +t(-4, 3, 1) intersects the plane -4x + y – 5z = 76.

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Q: Find the point on the line 6x + y = 6 that is closest to the point (-4, 1). (x, y) = %3D

A: We have to find a point on the line 6x + y = 6 that is closest to the point (-4,1). Concept Used -…

Q: Find a plane containing the point (-4,-4,6) and the line of intersection of the planes -x + 3y – 2z…

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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 distance from the point to the plane.   (4,1,8)​, 7y+5z=0

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Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, - 1, 2) is parallel | to the line x=…

A: Given that points are (2,1,-1), (0,-2,0) and (1,-1,2) The parametric equation is,…

Q: Find the distance of the point (3,8,2) from the line , -y+3 -z+2 Q2: measured parallel to the plane…

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

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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: Find the point on the plane x−3 y+3 z =−8 that is closest to the point (−2,−2,0) .

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Q: Find an equation of the plane whose points are equidistant from (6, -5, 3) and (7,5, 5). 13x + 8z –…

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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 point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

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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 distance from the point (-6,2,-7) to the plane -x + 4y = 2z = 22.

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Q: Find the distance from the point (2,-3,5) to the plane passes through the points (1,0,-3), (3,4,-6)…

A: (b) Given point P2,−3,5 and a plane passes through the points 1,0,−3, 3,4,−6 We have to find the…

Q: What is the equation of the plane through the point (4, -2, 3) and parallel to the plane 3x - 7z =…

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Q: Find the equation of the plane that contains the line 2 5-x 2+y – 5 – z, and the 3 point P( 0,5,2).…

A: We have to find the equation of the plane that contains the line and the point.

Q: Find the point at which the line (-4, –5, 2) + t(-4, 3, –5) intersects the plane 2x + 5y + 4z = -6

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Q: Solve for the linear equation of the plane through the point (1,9,10)(1,9,10) and parallel to the…

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Q: Find a plane containing the point (-4,-7,3) and the line of intersection of the planes - 2x + 7y +…

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Q: Find the linear equation of the plane through the point (0, 1, 1), (1, 0, 1), and (1, 1, O)

A: Consider the point (0,1,1). Take option (a) x-y-z+2=0-1-1+2=0 Take option (b) -x+y-z+2=-0+1-1+2=2≠0…

Q: Find an equation of the plane. The plane that passes through the point (-3, 3, 3) and contains the…

A: Given,            The plane passes the point -3, 3, 3 and also contains the line of intersection of…

Q: Find the coordinates of the intersection point of the lines x_1 + 3x_2 = 3 and −2x_1 + 4x_2 = 1 in…

A: Solved below

Q: find the distance from the point (2,2,3) to the plane 2x+2y+2z=4

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Q: Find equation of the plane through (1,0,-1).(-1,2, 1) and parallel to the line of intersection of…

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given…

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Q: The line passes through the point(7, 8, 9) and is parallel to the xz-plane and the yz-plane. 7,8,1 +…

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

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Q: Find the distance from the point (-2, 1, 4) to the plane x = 3

A: Given: The point -2,1,4 and plane x=3 To find: Distance from the given point to the given plane.

Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, -1, 2) is parallel to the line x 1-t,…

A: equation of plane for non collinear points , x-x1y-y1z-z1x2-x1y2-y1z2-z1x3-x1y3-y1z3-z1 we will use…

Q: The distance from the point S(-7, 8, -4) to the plane 10x+2y+11z=2. 20 3 8 15 8 225

A: The equation of the plane is  10x+2y+11z = 2 The point is S-7,8,-4 To evaluate : The distance from…

Q: Find the equation of the line perpendicular to the plane x−2y +z = 4 passing through the point (1, 0

A: We have to find equation

Q: 1. F = [2², -x², 0], S the rectangle with vertices (0, 0, 0), (1, 0, 0), (0, 4, 4), (1, 4, 4)

A: As given that,  F→=z2i^-x2j^+0k^ Calculating curl F,…

Q: Find an equation of a plane through the point (-2, 1, 5) which is orthogonal to the line 2= -3- 3t,…

A: The director vector of the line is (-3, -4, -3). Given that the plane is orthogonal to the line. So…

Q: Find a plane through the point Po(2, 1, -1) and perpendicular to the line of intersection of the…

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Q: Find an equation of the plane that passes through the points (-2, 1, 1), (0, 4, 7), and (1,0, –1).…

A: The plane that passes through the point,       -2,1,1, 0,4,7 and 1,0,-1

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.