Find the line of intersection of the given planes. 4x + y – z = 0 and 2x - y + 3z = 4 y = 2 + t 2

Q: Find a plane containing the point (6,-7,7) and the line x(t) y(t) z(t) = = = - 2 - 6t - 1 + 5t 5-t

A: Here we have to find the equation of plane

Q: Determine if the line intersects the plane. If so, state the solution. [x, y, z ] = [− 1, − 9, 16]+t…

A: The given line is [ x, y , z] = [ -1, -9, 16]  +  t   [ 3, 3, -5]  and the given plane is x+4y+3z=11…

Q: Find the equation of the plane through (1,-4,2) and per pendicular to each of the planes 2x t 5y -2…

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Q: find the line of intersection (if any) of the given planes. x+3y +2z - 6 = 0, 2x – y + z+2= 0

A: Given,         The equations of two planes are           x+3y+2z-6=0          2x-y+z+2=0

Q: Which of the following is the equation of the plane where x-2y + 32 = 3 and x+y+z=2 and passes from…

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Q: Which of the following planes contains the z-axis?x + y = 1

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Q: Find the intersection of the planes r + 2y - 3z 1 and x -y+ z 1 two different

A: Given: equation of planes We need to find intersection of above two planes.

Q: Find a plane through P0(2, 1, -1) and perpendicular to the line of intersection of the planes 2x + y…

A: The directional vectors of the planes are given by (2,1,-1) and (1,2,1)The directional vector of the…

Q: O Determine if the line and plane intersect. If so, state the solution. T: -2x+6y + 4z_4=0 L: [x, y,…

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Q: find the line of intersection (if any) of the given planes. x+3y+2z-6= 0, 2x – y+z+2= 0

A: The equation of plane are x+3y+2z-6=0 2x-y+z+2=0

Q: Q2/ Find the equation of the plane through the point (2, 4, 5) perpendicular to the line: X=5+t,…

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Q: 5. (a) Find an equation for the line of intersection between the planes r+3y-z = 2 and 2x – y+2z =…

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Q: Q3/ Find the equation of the plane that contains the line 3-x 2+y %3D 3 - z, and the point P (1, 4,…

A: Given line is  3-x4=2+y2=3-zand the point is (1,4,3) find the equation of the plane

Q: Find the intersection of the following geometric objects: the plane 3x + 2y - z = -9 and the line…

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Q: Which of the following is the intersection point of the plane 5x- 2y- 3z=0 and X = 6+ 2t the line y…

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Q: (a) Find an equation for the line of intersection between the planes x+3y–z= 2 and 2x –y+2z = 5. (b)…

A: Given: Two planes  x+3y-z=2vector a = <1 , 3 , -1 >2x-y+2z=5vector b = <2 , -1 , 2 >

Q: The line (x-22-3, y = 2z) intersects the plane (x+3y-2+4= 0) at the point P, Find: a) the…

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Q: The planes x - 2y + 32 - 3 =0 and 3x + y - z + 5 =0 are perpendicular. Select one: True False

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Q: Q8) The distance between the line x=-1+t, y3D3+2t, z=-t and the plane 2x-2y-2z=3 is: *

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Q: b) Determine, showing steps, whether the line [x, y, z] = []+¹] intersects the plane: 3 x + 7y + 8z…

A: We have to find the intersection of plane and line.

Q: The line L(t) = (3+t, 12+5t, -12-5t) intersects the plane 5x - 5y = 15 at what point?

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Q: Find the point of intersection for the following three planes: x - 2y + z + 6 =0 2х + у — z + 2 %3D0…

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Q: 1. Find an equation of the perpendicular bisector of the segment joining(3. -1) and (-1. 7). (A) x +…

A: Here we have to find the equation of line which is perpendicular bisector of the segment joining(3.…

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

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Q: Given the point P (2, 4, -1) and the line L: x 1+ 2t; y =2-5t; z 2 +3t Find the equation of the…

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Q: (50p.) l- Find an equation of the plane through (1,3,–2) and the line of intersection of the two…

A: Given that, P1 : x-y+z=1 P2 : x+y-z=1 and Point A(1,3,-2)   We have to find Equation of Plane…

Q: C. Find the equation of the plane passing thru P;(-1,2, –3) and perpendicular to the line through…

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Q: N. H. Name the intersection of ONJ and KJI. Name the intersection of KOL and MLH. Name two planes…

A: The given figure is We have to a) Name the intersection of ONJ and KJI b) Name the intersection…

Q: (b) Find the points where the line passing through (-2,0,1) and (-4,1,4) intersect the sphere x2 +…

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Q: H.W 2- Determine the points of intersection of the given line and the three coordinate planes. 1. x…

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Q: H.W: Find the point where the line 8 x=+ 2t , y= -2t , = 1+t intersects the plane 3x + 2y +6z = 6

A: Given that:                    The line with equation:      x=83+2t, y=-2t, z=1+t     & Plane:…

Q: Find the distance from the point Q= (2,2,2) to the line of intersection of the planes x+y+z=1 and…

A: Distance from the point Q(2,2,2) to the line of intersection of planes x + y + z = 1 and x + y = 2

Q: Find the point o

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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)…

A: The equation of the plane passing through the points (x0 , y0 , z0) and perpendicular to a vector…

Q: Find the equation of a) the line passing through the point (2, 1, 0) and parallel to the line X =…

A: Find the equation of (a) the line passing through the point 2,1,0 and parallel to the line x=5+2t ,…

Q: (a) Find an equation for the line of intersection between the planes z+3y-z = 2 and 2x –y+2z = 5.…

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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: Q/ Find the angle between the planes (x+y+2=1)and (x-24+32%-1).And find the Symmetric equations for…

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Q: The wedge cut from the cylinder, x2 + y? =1 by the planes, z = -y and z = 0. Set up only

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Q: Q/ Find the angle between the planes (x+y+Z=1)and (x-2y+32=1). And find the Symmetric equations for…

A: We have to find angle between two planes

Q: Find the point of intersection for the following three planes: 3x + 4y + z + 4 =0 x + 2y + 3z +2 = 0…

A: Given Planes:

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: Find the equation of the line of intersection of the following two planes: Plane A: 2r – 3y + 2z =…

A: Given Plane A : 2x - 3y + 2z = 5Plane B : x + 2y - z = 4To find the intersection point, Put z = 0 ,…

Q: Find the equation of the line of intersection of the planes 2x+y-2z = 1 and x+2y-z = 4.

A: Planes are 3-dimensional spaces, that contains infinite lines. When two non-parallel planes…

Q: B. If the two planes ax-4y - 9z = 4 and perpendicular. Find the value of a. x-2xy + 3z = 1 are

A: Topic = Geometry

Q: find the line of intersection (if any) of the given planes. x+3y+2z - 6= 0, 2x – y + z +2= 0 O a.…

A: Answer

Q: Which of the following are symmetric equations for the line of intersection of the planes 2x+y+−6z=2…

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Q: The planes x + 2y + 3z = 12 and 2x + 3y + z equation is (x, y, z) = (0, 6, 0) + n(7, – 5, 1). Find…

A: Equation of a line in space :  r→ = a→ +n b→  , where…

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.