the xyz-plane determine the distance and angle from point (2,1,1) in the space and two planes (x-y-2z=9) and ( x+y+z=4

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

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane given…

A: Given problem:- Find the point of intersection of the line through (1,-3, 1) and (3,-12, 6), and the…

Q: Formulate the equation of plane in space that contain two points (2,4, -1) and (1,3, -2) and…

A: Steps 1. Write down the position vector a→ and b→ through which the plane is passing. 2. Equation of…

Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

A: Given  P1 = (10,-8,5) From equation we have point passing through line and parallel vector

Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with .the xy-plane,…

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Q: ear equation of the plane through the nts (6, 3, 2) and (4, −1, 1).

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Q: Find an equation of the plane through the point (3, -5, 1) and parallel to the plane 4x − 5z = 12

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Q: Find an equation of the plane that passes through the points (2, 4, 1), (2,2, –4), and (-–3,5, 3).…

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

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Q: etermine the intersection point of the two lines or show that they do not intersect. a. Does the…

A: Given: (-5,4,-1) and (-3,-5,0)

Q: ....... Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane…

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Q: Find the distance from the point (3, 3, 5) to the plane 3x - 3y + 3z = 5. Leave your answer correct…

A: topic- distance of a point from a plane

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

A: Find equation of line and put parametric value of (x,y,z) in plane and solve for x,y and z.

Q: A perpendicular line is drawn from point P(1,2,1) to the plane -2x+ 4z 8 and meets the plane at…

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Q: Find the equation of the plane that is parallel to the vectors 3,0,1 and 0,1,2​, passing through the…

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

A: Distance between the point x1,y1,z1 and the plane ax+vby+cz+d=0is given by-d=ax1+by1+cz1+da2+b2+c2

Q: Locate the point of intersection of the plane 2x + y - z = 0 and the line through (4,2,0) that is…

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

A: We have to find a point on the plane closest to another point.

Q: Equation of the plane passing through the point (4, –2, –1) and parallel to yz-plane is

A: To find the equation of the plane passing through the point 4, -2, -1 and parallel to yz-plane.

Q: 2. Obtain an equation for a plane 7 that includes straight line(2"--5) and point(-2,1,1).

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Q: Find the coordinates of a point that is located five units in front of the yz-plane, three units to…

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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: Let a rectangular a'y'z'-coordinate system be obtained by rotating a rectangular xyz-coordinate…

A: The standard transition matrix from B to B' is given by: P=cosθ-sinθ0sinθcosθ0001

Q: Find an equation of plane through the points pl (-1, 1, 1) and point of intersection of the plane 2x…

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane given…

A: Given the point (1,-3,1) and (3,-12,6) and the plane x-y+z=6

Q: Find the point of intersection of the line through (1, -5, 1) and (5, -12, 6), and the plane given…

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Q: Find equation of plane that contains the points (-1, 2, 1), (0, -3, 2), and (1, 1, -4)

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Q: Consider the point. (4, 5, 6) What is the projection of the point on the xy-plane? (х, у, 2) 3D (|…

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Q: 1. A line, passing through point (6, 3, 2) and is perpendicular to the yz-plane. Find a point on…

A: Question is solved step by step.

Q: Your friend drew the diagram to prove to you that two planes can intersect in exactly one point.…

A: A point is a zero-dimensional object. The point does not have a length. A line is obtained from…

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: How to find an equation of a plane through a specific point such as (3,0,3)?

A: There can be infinitely many planes passing through one point and hence you can not find an equation…

Q: Find the coordinates of the point. The point is located in the yz-plane, seven units to the right…

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Q: (1 point) Find the point at which the line (-2, 1, –5) + t(-1,–1, –2) intersects the plane 4x – 2y +…

A: To findcthe point at which the line (-2,1,-5)+t(-1,-1,2) intersects the plane 4x-2y+2z=-68

Q: 3 Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with the xy-plane,…

A: The given equation of lines are  x = - 2, y = 4 +2t z = - 3 + t

Q: A line is drawn through the point (6,4,2) perpendicular to the yz- plane. Find the coordinates of…

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Q: 5. The line passes through the point (-4, 5, 2) and is parallel to the xy-plane and the yz-plane. 6.…

A: Solution for a: Since line passes through the point P(-4,5,2) and parallel to xy-pane and yz-plane.…

Q: What is the equation of the plane containing the points (1,−2,0) , (3,1,4) and (0,−1,2)?

A: The equation of the plane containing the points (1,−2,0) , (3,1,4) and (0,−1,2)

Q: Find symmetric equations for the line through the point (1, -2, -4) which is orthogonal to the plane…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

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Q: Equation of the plane passing through the point (3, –2, 5) and parallel to yz-plane is

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

A: Given : the equation of a plane is  x-y+z=5  and the line passes through (1, -4, 1)  and (4, -10,…

Q: Consider the point. (3, 5, 6) What is the projection of the point on the xy-plane? (x, y, 2) = What…

A: given point is (3,5,6) find the projection on xy, yz , zx planes  also find the length of diagonal…

Q: Find a plane containing the point (-4,4,2) and the line of intersection of the planes -3x + 8y + 2z…

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Q: find the equation of a sphere passing through the point(1,-3,4),(1,-5,2),(1,-3,0) and having on the…

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Q: Show that the plane through (1,1,1) and (-7,-3,-5) is parallel to Y-axis

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -8, 4), and the plane given by…

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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.