et L be a line which passes through the point (-3,0, 1) and is perpendicular to the plane z + 2y+3z=0. ind the y coordinate of the point of intersection of L and the plane 6z – 3y + 2z = 14

Q: Consider the line which passes through the point P(-3, –3, –1), and which is parallel to the line x…

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Q: 25. Find the intersection of the line [x, y, z] 2х — 4у + 7z —26 %3D 0. [1,4, – 2] + t[1, – 1,3] and…

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Q: point A (-5, 3, 7) to the plane v = (0, 0, 2) + t (-1, 1, 3) + s (2, 0,-3) and determine the…

A: The cartesian equation of the plane is given as follows                v→…

Q: Locate the point of intersection of the plane 2x + y−z = 0 and the line through (3, 1, 0) that is…

A: Our Aim is to locate the point of intersection of the plane 2x+y-z and theline through (3,1,0) that…

Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

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Q: Find the line r that passes through the origin and is perpendicular to the π planes that passes…

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Q: (A) Determine the plane that contain the point A(2,5,1) and the line L, t=x-2, 3t =y-1, t=z+1

A: The equation of the line L given in the parametric form, that is, Thus, the above equation of the…

Q: Let p be a plane which contains the point Q(1,2,3) and the intersection line of the planes: 2x+3y-…

A: Concept: 1. The equation of plane passing through the line of intersection of the given planes…

Q: What is the distance between the point A(2,5,1) and the plane x + 2y +2z +1=0 ? Answer:

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Q: Find a plane through P (2, 1, 1) and perpendicular to the line of intersec- tion of the planes:…

A: find a plane through P2,1,1 and perpendicular to the line of intersection of the planes  2x+y-z=3 ,…

Q: Find the symmetrical point of point P(-1,-3,5) with respect to the plane D:3x-2y+z+6=0

A: Point P(-1,-3,5)  plane D:3x-2y+z+6=0

Q: (6) Where does the line through (1,0, 1) and (4, -2, 2) intersect the plane r+y+ z = 6?

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Q: Find a plane through the origin that is perpendicular to the plane M: 2x + 3y + z = 12 in a right…

A: Given equation of plane is

Q: 3. Find the plane determined by the intersecting lines L: x = -1+t, y = 2+t, z = 1- t; L2: x = 1 -…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: What is the intersection of the plane x+2y+z =0 and the line (x, y,z) = (0,1,2)+ k(–1,1,2), kER?

A: Consider the equation of plane x+2y+z=0 and the equation of line x,y,z=0,1,2+k-1,1,2. Find the…

Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane r + 2y +…

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Q: A) What is the point of intersection between the plane x – 2 y +3 z +1 = 0 and the line r = + t? B)…

A: Use substitution method

Q: Where does the line through (1, 0, 1) and (4, −3, 3) intersect the plane x + y + z = 6?   (x, y,…

A: Given points are Given Plane is

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane z + 2y +…

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Q: Find the symmetrical point of point P(1, 3, 4) with respect to the plane D:3x-2y+z+6=0.

A: Symmetrical point at plane problem....

Q: Find the distance between the given point and the given plane. Point: (−1, 4, −2) Plane: x+2y+z=3

A: We can use distance formula to calculate the distance.

Q: Consider the line which passes through the point P(5, 2, -1), and which is parallel to the line x =…

A: Introduction: In three dimensional geometry, there are three fundamental planes referred to as the…

Q: Find the point of the intersection of the plane P: 2x- 3y + 4z + 14 = | 0 and the line L:x =1-t, y =…

A: See the attachment

Q: (31) Find a plane through A(2, 1, –1) and perpendicular to the line of intersection of the planes 2x…

A: Given, 2x+y-z=3 ,x+2y+z=2 The equation of the plane passing through x1,y1,z1 is given by…

Q: Find an equation of the plane. the plane that contains the line x = 2 + t, y = 3 - t, z = 5 - 3t and…

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Q: ind the equ.of Plane that Contains plos1,3) and Parallel to the X-2 Plane and PerPendicular to the…

A: Solution:-

Q: The Line whose eqs are ," X-2Z-3=o the plane X + 3y-Z+4=0 and y - 2 Z=0 in Lersecs Find the point of…

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Q: Find an equation of the plane. The plane that passes through the line of intersection of the planes…

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Q: Find the points of intersection of the line x = 3 + 2t, y = 7 + 8t, z = -2 + t, that is, I(t) = (3 +…

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Q: 4. Consider plane P: 4x – y+ 2z = 8, line l: (x, y, z) = (1+t, –1+ 2t, 3t ), and point Q(2, –1,3).…

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Q: Find an equation of the plane. The plane that contains the line x = 3 + 2t, y = t, z = 6 - t and is…

A: We will find the equation of planes.

Q: Find the point where the point P(1,3,4) is symmetrical with respect to the plane D:3x-2y+z+6=0

A: In this question we will use basic of geometry i.e image of a point in a plane. Solution of the…

Q: Find the distance from the point B = (1, 0, 2) to the plane P whose general equation is x + y -z =…

A: Equation of the plane is Given point is

Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: Find the distance from the point to the plane. (5,7,6), 10y +z= 0 The distance is

A: We can find the distance as below.

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

A: Given x=-2, y=4+2t, z=-3+tfor finding intersection with xy-plane , set z-coordinate…

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane r+ 2y +…

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

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

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Q: Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (3,– 1, 7)…

A: Given: Parametric equation of line l: (x,y,z)=(3,-1,7)+r(-5,2,1) Equation of plane: 2x+3y+4z=24

Q: Find the angle between the plane -2x +y-2z 0 and the plane generated by the points P1(0, 0, 0),…

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Q: Check that the line (1,0,1)+t(3,0,1) is parallel to the plane -2x+4y+3z=13 and calculate the…

A: For the equation of the plane , the direction vector of the normal to the plane is given by . For…

Q: 4. Find the point of intersection of the plane z= 4 and the line L={ (x, y, z) | x= 4 + 3t, y=-1-2t,…

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Q: The plane can perpendicular to the a) x-axis at (3, 0, 0) b) z-axis at (0, 0, -2) c) y-axis at (0,…

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Q: Find the distance from the point to the plane. (7,3,6), 10y +z= 0 The distance is

A: Given query is to find the distance between the point and the plane.

Q: Let S be the plane with the equation x + y – 3z – 6 = 0. - Find the distance between this plane and…

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Q: Find the point of intersection of the lines x t, y = -t + 2, z = t + 1, and x 2s + 2, y s + 3, z 5s…

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Q: 25. Find the intersection of the line [x, y, 2] = [1,4, – 2] + 1(1, – 1,3] and the plane 2r – 4y +…

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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.