Find an equation of the plane containing the lines L1 and L2 in R3 L1: x = t ; y = -t ; z = t L2: (x-3) /2 = y = z - 2

Q: The point of intersection between the line t with the plane 2x + 3y +5z = 31 is

A: Given line ,x-1-4=y-13=z5=tTherefore any point on the line is of the form (1-4t,1+3t,5t)Put this…

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

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Q: find the plane containing the intersecting lines.  L1: x = t, y = 3 - 3t, z = -2 - t; -inf < t…

A: This question is taken from the planes in which we have to find the plane equation. We can write the…

Q: Calculate the equation of the line that passes through the point (0, 1, 2) that is parallel to the…

A: We need to find the equation of the line passing through a point, parallel to a plane and…

Q: Find equation of the plane that contains the lines L1:x = 3 + 5t, y = 6+ 2t, z = 6 + 3t and L2: x =…

A: Equation of plane which passes through L1 is ax-3+by-6+cz-6=0 where 5a+2b+3c=0.

Q: Find an equation of the plane that contains the point P(5,0,2) and the line x = 3t +1, y=-2t + 4, z…

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Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1and 2x+3y+4z=…

A: The equation of the plane through the intersection of the planes, x+y+z=1 and 2x+3y=4z=5, is…

Q: Find the equation of a plane through the point (- 1,1, 3) and orthogonal to the line ( x(t) = – 7 –…

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Q: Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = 0.

A: Given Line is x=1+t,y=2t and z=-3t  And Given plane is x+y-z=0

Q: Find an equation of the plane that contains the line l(t) =(-1,1,2)+t(3,2,4)y which is perpendicular…

A: As given by the question There are given that the equation of line: lt=-1, 1, 2+t3, 2, 4 And, The…

Q: Find the equation of the plane that contains the line x=-1+3t, y=5+2t, z=2-t and is perpendicular to…

A: topic - equation of plane

Q: Find the distance from the line x = 2 + t, y = 1 + t, z = -(1/2) - (1/2)t to the plane x + 2y + 6z =…

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Q: Find the point P where the line x = 1 +  t,  y  =  2t,  z = - 3t  intersects the plane x + y - z =…

A: Given line: x=1+t,  y=2t,  z=- 3t

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

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Q: Determine the equation of the plane that contains the lines Li and L2. L: x = 3- t, L2: x = 8 +2 s,…

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Q: Find the plane that contains the point (0, 1, 2) and the line x = 1- t,y = 2 + t,z = 4 + 3t.

A: Here I am attaching image so that you understand each and every step.

Q: Find a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

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Q: Find the point P where the line x = 1+t, y= 2t, z= -3t intersects the plane x+ y -z = -3

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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: equation

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Q: Find the point of intersection of the line l: x = 2+ 3t, y = 1 – 6t, z = 4 – 2t with the plane - 2x…

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Q: Find the point where the line x=8+2t, y3-2t,z=1+t intersects the plane 3x+2y+6z36.

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Q: Find the point(s) of intersection (if any) of the plane 2x + 3y = 10 and the line (x − 1)/3 = (y +…

A: The equation of line x-13=y+1-2=z-3=r(arbitarary point) then x = 3r +1 y = -2r -1 z = r+3

Q: / Find the distance from the line x 2 + 1, y 1 +1, z = -(1/2) - (1/2)t to the plane x + 2y + 6z 10.

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Q: Find an equation of the plane that contains the line x = −2 + 3t , y = 4 + 2t , z = 3 −t and is…

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Q: Find an equation of the plane containing the lines given by 1-x = y = z+ 1 2 and * = y – 1 = z - 2…

A: From the given problem:, the plane containing lines are: 1-x2=y=z+1andx+1-2=y-1=z-2 So we can simply…

Q: Find the equation of a plane through the point(- 3, – 2, 3) and orthogonal to the line x(t) - 5+ 8t…

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Q: Find the distance between two lines (L1: x=3t-1, y=t+6, z=2t+3 and L2: x=2t+6, y=2t+11, z=-t+3)…

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Q: find the point in which the line meets the plane x = 1 - t, y = 3t, z = 1 + t; 2x - y + 3z = 6

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Q: Find an equation of a plane through the point (0,−2,1) which is orthogonal to the line…

A: The equation of a plane passing through the given point is as follows.

Q: Find the point of intersection of the line x = 2 − 3t y = 4 + 2t −∞ < t < ∞, z = 3 − 5t, and…

A: x=2-3ty=4+2tz=3-5tand the plane 2x+3y+4z+8=0

Q: Find the point in which the line through the (3,-1,2) perpendicular to the plane x +2y -5 z = 4…

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Q: ) At what point does the line: L: x =- t, y = 10 + 3t, z = 4 + 3t intersect with the plane n: x – 2y…

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Q: Find the point of intersection between the line r(t) = + t and the plane 4x + 5y + 3z = 5. o a. (…

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Q: Find the equation of the line containing the point (1, 3, −2) that is parallel to both of the planes…

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Q: Find the general equation of the plane that contains the point (2, 0, 3) and the line x =−1+t, y =…

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Q: Find the equation of the plane containing the line: x = 2 + 10t, y = 2 – 2t, z = 9 + 4t and parallel…

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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: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

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Q: The intersection point of the line whose equation is (x+2y+z=1),(x+y+2z=-1) with the xz plane is:

A: we have given x+2y+z=1  ...(i)x+y+2z=-1  ...(ii)solve it  2×(i)-(ii)x+3y=3   ...(a) this is equation…

Q: . Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 2+8 L1 : 4 -t…

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Q: Find the point in which the line through the origin perpendicular to the plane 2x - y - z = 4 and…

A: Your line, perpendicular to the plane will have the slope of <2, -1, -1>, and passes through…

Q: Find an equation of the plane that is passing through the point and is perpendicular to the line L.…

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Q: Find the point at which the line intersects the given plane. x = 4 - t, y = 5 + t, z = 3t; x - y +…

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Q: Find the intersection of the line 1₁: x-6 2 || y+2 1 with the plane p: x-6y - 2z - 10 = 0

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Q: . Find the equation of the line containing the point (1,3, –2) that is parallel to both of the…

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Q: Give the general form of the equation of the plane that is perpendicular to the plane x+2y x-4 1-2y…

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Q: Find an equation of the line normal to the plane containing the line I-2 y+1 %3D and +1 - y+8 %3D 3…

A: The given problem is to find the equation of line normal to plane containing the lines at their…

Q: Does the line r(t) = intersect the plane 5x - 2y - z = 21 and if so, where?

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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.