Let L1 be the line through the points ( 1 , 2 , 6 ) and ( 2 , 4 , 8 ). And let L2 be the line of intersection of the planes π1 and π2 , where π1 is the plane ( x − y + 2z + 1 = 0 ) and π2 is the plane through the points ( 3 , 2 , −1 ) ( 0 , 0 , 1 ) and ( 1 , 2 , 1 ). Calculate the distance between and L1 and L2 .

Q: Let L, be the line through the points (1. 2. 6) and (2, 4, 8). Let L, be the line of intersection of…

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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: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

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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: Let L be a line which passes through the point (-5,0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let T, denote the plane parallel to the xz-plane through the point (1, 2, 3). Let n2 denote the…

A: To solve this problem first of we find the equation of the plane π1 and π2 in standard form and then…

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: 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: Let L be a line which passes through the point (-8,0, 1) and is perpendicular to the plane a + 2y +…

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Q: Find an equation of the plane through (-3, 8, – 7) that is perpendicular to the planes 6x – y +z = 4…

A: We need to find equation of plane.

Q: 5) Find the distances: a. Between l, = (2 + 2t, –1+ t,–3t) and l, = (4,–5 – 3t, 1+ 4t). %3D b.…

A: Given: (a). two lines l1 and l2 (b). Two Planes (c). A point (1,2,3) and a line  To Find: (a).…

Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

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

A: In xy plane z = 0 = t - 3. Therefore t = 3 so the point of intersection is (-2,10,0). Similarly.

Q: Let L be a line which passes through the point (-5, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: 24. The plane that contains the line x = 1 + t, y = 2 – t, z = 4 – 3t and is parallel to the plane…

A: To find out equation of plane first we change the equation of line in symmetrical form then find out…

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: Let L be the line x = t, y = -11 - 7t and z = -6 - 3t and let M be the line x = 1 +s, y = 2s and z =…

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

A: Given lines are x=2t+1, y=-t+2, z=t+1x=2s+2, y=s+3, z=5s+6

Q: Find the distance between the line 2x - 3y + z = 6, 2y- z = 4, and the plane passing through the…

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Q: 2. Find the plane that is orthogonal to the line : +1 = 431 = z and contains the point where l…

A: line parallel to the vector  V=⟨a,b,c⟩ passing through the point (x1,y1,z1) is given by 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 through (– 1, 3, –4) that is perpendicular to the planes 8x – y + z =…

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Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

A: Here we will find Z-coordinate of intersection L with given plane,

Q: Let L be the line that passes through the point  (1,3,1 ) and orthogonal to the plane 3x-2y + 5z =…

A: In the question we have to find interacting points at which line and plane intersect.

Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane a + 2y +…

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Q: 12) Find the intersection of the plane: x – z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

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Q: Find the plane containing the intersecting lines x = -1+t, y = 2+ t, z =1–t; -0 <t < o∞ | L2: x = 1…

A: Find the planes containing the intersecting lines: L1:x=-1+t,y=2+t,z=1-t for all…

Q: Let L, be the line through the points (1,2,6) and (2,4,8). And let L2 be the line of intersection of…

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

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Q: Let L be a line which passes through the point (-8,0, 1) and is perpendicular to the plane z + 2y +…

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Q: 2. Find the eanation of the plane Containing the point (2,3,3)'and the line Of intersÉCtion 'of the…

A: We have to find the equation of plane containing the point (2, 3, 3) and the line of intersection of…

Q: 31. Determine the point of the plane T: 15x - 3y + 2z + 6 = 0 intersection of the line [x, y, z] =…

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Q: 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two…

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Q: Show that the line in which the planes x + 2y - 2z = 5 and 5x - 2y - z = 0 intersect is parallel to…

A: Find the vectors normal to the planes x + 2y - 2z = 5 and 5x - 2y - z = 0.

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

A: Given, The line x = -2,  y = 4+2t ,  z = -3+t   We have to find the points of intersection of line…

Q: Let L be a line which passes through the point (-5,0, 1) and is perpendicular to the plane x + 2y +…

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Q: Find the distances (a) Between l1 = (2+ 2t, –1+t, -3t) and l2 = (4, -5 – 3t, 1+ 4t) (b) Between the…

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Q: Q3/ Find the plane determined by the interseetiny Lines L X=1-2t, , 3-st,,そニ-2+t, La.Xe-3+t2)…

A: To find equation of plane we need to first find point and direction ratio of lines. Then find…

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

A: Here we find the equation of line L and also find the intersecting point of line and plane.

Q: Find the plane determined by the intersecting lines. L1 x= - 1+ 3t y =2 +3t z =1- 4t L2 x= 1-4s y =…

A: Given :-  The plane determined by the intersecting lines. L1    :   x = -1 + 3t    ,    y = 2 + 3t…

Q: Show that the line in which the planes x + 2y – 2z = 5 and 5x – 2y - z = 0 %3D intersect is parallel…

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

A: The line L is perpendicular to the plane, x+2y+4z = 0 Hence the direction ratios of the line L is…

Q: Let L be a line which passes through the point (-3, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let L1 be the line through the points (1,2,6) and (2,4,8). And let L2 be the line of intersection of…

A: We have to find the distance between line L1 and L2.

Q: Find the point of intersection of the lines x = 2t + 1, y = 3t + 2, z = 4t + 3, and x = s + 2, y =…

A: Equate the x and y coordinates in t and s domain to obtain values for t and s.

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: Let L be a line which passes through the point (-5,0, 1) and is perpendicular to the plane * + 2y +…

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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.