Consider the line which passes through the point P(5, -5, 5), and which is parallel to the line x = 1+ 4t, y =2+1t, z = Find the point of intersection of this new line with each of the coordinate planes: 3+ 3t

Q: Consider the line which passes through the point P(1, -3, -2), and which is parallel to the line x =…

A: Given: The vector equation of the line is: x=1+4t;y=2+7t;z=3+1t r→=123+t471 so the line is the…

Q: (B.) Determined by the intersecting lines L1 and L2 L1 : {x = 2t, y= 4- t, z = 3 +t}and L2:{x = 2 +…

A: According to guidelines we solve one question. thanku.

Q: For the line 2x + 3y = 6, find a line parallel to it containingthe point 11, - 12. Also find a line…

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Q: Verify that the lines are parallel, and find the distance between them L1: x = 2 - t, y= 3 + 4t, z =…

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Q: Find an equation of the line that satisfies the given conditions. Throught (2,6); perpendicular to…

A: y=1;(2,6)

Q: Sketch the lines 3x+ 4y 7 and x- 2y = 6, and find their point of intersection. Hint: Their point of…

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Q: If C is the line segment connecting the point (a1, b1) to the point (a2, b2), show that 3r dy – 3y…

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Q: Ex(29):- Determine whether the line and the plane are intersect; if so, find the point of the…

A: Given, The equation of the line   L : x=t, y = t, z =t  Equation of the Plane : PL : 3x-2y+z-5=0…

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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

A: Equation of the line :       x-x0a = y-y0b = z-z0c=k ; where x0,y0,z0 is a point and a,b,c is the…

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

A: Answer

Q: parallel

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Q: Find the distance of the point (3, 2, –4) from the line r(t) = (1+ 3t, –1+ 2t, 3 – 3t).

A: for finding distance of the point3,2,-4 from line rt=1+3t, -1+2t, 3-3t we assume a point1+3t, -1+2t,…

Q: The line in R that is parallel to the y-axis and passes through the point (1, 2, 3) has equation + t…

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Q: Show that the lines whose direction cosines are given by l+m+n=0,2mn+3nl-5lm=0 are perpendicular to…

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

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Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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Q: 1. Find the angle between the lines L,:x = 3 + 8t, y = -6t,z = –7+ 24t and L2:x = 3 + 8t, y = 15t, z…

A: Solving only ques 1 according to guidelines.

Q: Let A be the point with coordinates (-3, 2, -1) and let B be the point with coordinates (2, 0, 0).…

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Q: Find the distance of the point (2, 2, –5) from the line r(t) = (1+4t, –1+ 4t,7 – 3t) %3D swer:

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Q: If a line intersects the x-axis at 'r' and the y-axis at '1/r', at what point (x,y) does it…

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Q: We have the line whose equation is L: x+ 2 = y+ 3 = 1- Find the points of the line L with the…

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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…

A: we have to find the point of intersection of the given lines

Q: ) Find the equation of line of intersection of the following planes 3x – 4y + 4z – 29 = 0 , 6x – 8y…

A: Explanation of the solution is given below...

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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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: Consider the line which passes through the point P(1, 3, -5), and which is parallel to the line æ =…

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Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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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: Do the lines (x, y, z) = (5 + 2t, 3 + 2t, 1 - If not, how do you know? t) and (x, y, z) = (13 – 3r,…

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Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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Q: Let A be the point with coordinates (-2, -1, -1) and let B be the point with coordinates (2, 0, 0).…

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Q: Consider the line which passes through the point P(2 -3, -4), and which is parallel to the line x =…

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Q: Find (i) the undirected distance between point A and b, and (ii) the midpoint of the line segment…

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Q: Find x'z ds, where C is the line segment from (0,2,-3) to (6,0,-6) C

A: To find:∫Cx2z dsThe line segment is from 0, 2, -3 to 6, 0, -6

Q: Consider the line which passes through the point P(-2, 4, 3), and which is parallel to the line x =…

A: Consider a line  L1:x=1+7t,y=2+7t,z=3+4t Point : −2,4,3

Q: Verify that the lines are parallel, and find the distance between them. (Round your answer to three…

A: To find if the two lines are parallel using their normal vectors and finding the distance between…

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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

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Q: find point b (x,y) given that M (7,3) is the midpoint of line A(10,4) and b

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Q: Show that the following sets of points are collinear and find the equation of the line L containing…

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Q: 3) Determine the point(s) of intersection of the lines L₁: (3,1,5) + s(4,-1,2) and L₂: x = 4 + 13t,…

A: Given

Q: Q1/The line joining origin and point of inter section of the lines (x = 1 + 2t, y = -3 + 4t, z %3D =…

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Q: Given are two points [1,3] and (6, –1] in the plane. Which equation of the form a ·z + b•y+c=0…

A: (y-y1)/(y2 -y1) = (x-x1)/(x2-x1) (x1,y1 ) = (1,3) (x2,y2 ) =(6,-1) (y-3)/(-1-3) = (x-1)/(6-1)…

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: Show that the equation of the line in R' through distinct points (1, Y1) and (x2, Y2) can be written…

A: We have to show that the equation of the line in R2 through distinct points x1,y1 and x2,y2 can be…

Q: 1. Find the angle between the lines L1:x = 3 + 4t, y = 2 – 3t, z = 12t and L2:x = 8t, y = 2 – 15t, z…

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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.