A point in space let us have the line,L which equates to it Q(-1,1,1) To be z Find the equation of the plane that passes through the point,Q(-1,1,1) and encompasses the line L L: 1- 2x = 1-3y =+:

Q: We have two planes in IR, defined by equations I- 3y+z -7 and 2 +y+2z = 0. These two planes…

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Q: 1. Find the purametric euuatlous of the line that contains the point C,-3,5) and is Perpendicular to…

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

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Q: Line Li: 0.5C1- X)= 2 = 0.5z intersects the plane defined by B(2,237), C Cl,o, 12) at point P. Find…

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Q: The third question: Let Q be a point in space (1-,1-,1-) and let us have the line L whose equation…

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Q: The third question: Let Q be a point in space (1-,1-,1-) and let us have the line L whose equation…

A: For the solution follow the next steps.

Q: Find the equation for the plane through the points Po(- 4, -2, – 5), Qo (0,1,2), and Ro(4,3, – 1).…

A: The given points are :    P0 (-4,-2,-5) , Q0 (0,1,2) , and R0 (4,3,-1)      The vector equation of…

Q: A point in space and let's have the line L whose equation is Q(-1,0,1) let 1 L: 3- x = y = 4 4 It…

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Q: a) b) Determine the equation of the line of intersection of planes 1 and 2. Express your answer in…

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Q: Find the equation for the plane through the points Po(1, – 5, – 3), Qo(-3, – 5, – 1), and Ro(-…

A: -5x+4y-10z=5

Q: The line L: x = 3 + 2t, y = 2t, z = t intersects the plane x + 3y - z =-4 in a point P. Find the…

A: Given:

Q: Find the distance from the point (5, 5, 5) to the line x = 0, y = 5+ t, z = 5+t. Find the point P…

A: Explanation of the answer is as follows

Q: Two planes x+ y – 27 = 3 and 2x – 3y + z = 1 intersect in a line. a Find the Cartesian equation of…

A: (a) Given that planes are x+y-2z=3 and 2x-3y+z=1 The cartesian equation of the two lines is,…

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

A: Given problem:- Find an equation of the plane with the given characteristics. The plane passes…

Q: 5. Find the point of intersection of the given plane and line. Plane: 2x - y+3z=7 Line: x=-1+t y…

A: We have to find  point of intersection .

Q: Find the plane containing the intersecting lines: L1: x = -1 + t, y = 2 + t, z = 1 - t; -∞< t < ∞…

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Q: Find an equation of the plane with the given characteristics. у — 4 The plane passes through the…

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Q: c)[ Find the equation of the plane through the point (5, 1, 0) which is parallel to the lines x = 2…

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Q: 24. Let A = (2,1) and B = (-1, –2) be two points on the plane. Write the equation of the line which…

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Q: Let Q(1,10,-1) be a point in space and a let us have the line L whose equation is 1 L: 1-x = 1- y :…

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Q: ] The plane contain the points P(1,-1,-4) and Q(2, 1,-3). Moreover, it contains the line I 2=y+3=…

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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: The endpoint of a line segment  is at  P1(–2, 1, 6)  and the  midpoint Q  lies on the plane  y = 3.…

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Q: Suppose the symmetric equations of lines l1 and l2 are = 2 - y = z and r = -1, 3 respectively. (a)…

A: If two lines are neither intersecting nor parallel then they are know as skew lines  If vector form…

Q: The line L: x = 3 + 2t, y= 2t, z = t Intersects the plane x + 3y – z = -4 in a point P. Find the…

A: The given line is: L: x=3+2t, y=2t, z=t The given plane is: x+3y-z=-4

Q: Find an equation of the plane. The plane that passes through the point  (−2, 1, 3)  and contains…

A: Question : Find an equation of the plane.   The plane that passes through the point  (−2, 1, 3)  and…

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

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Q: 9. A rhombus is drawn in the standard xy-coordinate plane. The line 2x+y= 4 includes one of the…

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Q: To be Q(-1,1,-1) L:1-x=2+y=z/3-5 Find the equation of the plane Which passes the point Q(-1,1,-1)…

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Q: L1 and L2 intersect in a single point. Find that coordinates of that point.  b) Find an equation…

A: In this question, we have three parts. (a) we find the intersection point by taking the general…

Q: The third question: Let (1-, 1-, 1-) Q be a point in space and let us have the line L whose equation…

A: Let the equation of the plane passing through the point Q-1,-1,-1 be ax+1+by+1+cz+1=0…

Q: We have two planes in R', defined by equations x – 3y + z = -7 and 2x + y + 2z = 0. These two planes…

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

A: A plane is the two-dimensional analogue of a point, a line and three-dimensional space.

Q: 3) The line L: x = 3 + 2t, y = 2t, z = t intersects the plane x + 3y -z = -4 in a point P. Find the…

A: To find the coordinates of P and find the equation for the line .

Q: Find the equation for the plane through the points Po(0,5,3), Qo(5, – 3,5), and Ro(2,1,5). Using a…

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Q: the

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Q: X ▪ Find equation of plane which is contains line L: 3y-2 2-7 = -3 -1 and parallel to intersection…

A: We will find a point vector on the plane a→ and normal vector to the plane n→ then equation of plane…

Q: 4. The equation of a plane is [x, y, z)=[-1,-1,1]+s[1, 0, 1]+[0, 1, 2]. Find the - intercept of the…

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Q: whose equation is L A point in space and let's Q(0,1, -1) let it be |have the line L: 3- 2x = 1- y…

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Q: Find the equation for the plane through the points Po(1, – 4, – 2), Qo(3, – 3,0), and Ro(5, - 1,0).…

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Q: a. Find an equation of the plane that passes through (3, 2, -1) and contains the line l(t)= (-t, 2,…

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Q: 22. a) Determine the equation of the line of intersection of planes 1 and 2. Express your answer in…

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Q: 3) The line L: x = 3 + 2t, y = 2t, z = t_intersects the plane x + 3y -z = −4 in a point P. Find the…

A: The equation of the line L is given as x=3+2t, y=2t and z=t. The line intersects the plane x+3y-z=-4…

Q: 6. Determine the point of intersection of the line l: = [-6,9,–1] + t[-2,3,1], t € R. and the plane,…

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Q: Find a point with z = 2 on the intersection line of the planes x + y + 3z = 6 and x - y + z= 4 .…

A: Given, equation of planes x+y+3z=6x-y+z=4

Q: Consider the points: A = (1,0,0), B : through the points A, B, C is (2, 3,5) and C = (-1,–3, –3).…

A: Use equation of plane

Q: Find the equation for the plane through the points Po(0, – 3, – 5), Qo (3, – 3, – 1), and Ro(5,2,0).…

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Q: I don't need any graphical explanation, just the work to solve works and I can figure it out from…

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Q: Po (2,1,-1) and perpendicular to the line of Find a plane that passes through intersection of the…

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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.