Consider the planes of equations -y+z - 2 = 0 and x- y = 0. a. Show that the planes intersect. b. Find parametric equations of the line passing through point P(-8, 0, 2) that is parallel to the line of intersection of the planes.

Q: Find parametric equations for the line through Po= (3, -1, 1) perpendicular to the plane 3x + 5 y -…

A: Given:  a Point Po =(3, -1, 1)  and a vector perpendicular to the plane is…

Q: Complete the parametric equations for the line where the planes – 3x – 9y – 12z - 11x + 2y – 10z 33…

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Q: Find a set of parametric equations for the rectangular equation that satisfies the given condition.…

A: Given :                y = 2 x - 5  ,  t = 0        at point (3,1)

Q: Complete the parametric equations of the line through the point (-6,0,-8) and perpendicular to the…

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Q: find the parametric equations of the line through (-3,0,2) that is parallel to 3i-4j+k. x(t)= y(t)=…

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Q: Find parametric equations of the line through (-3,0,9) that is parallel to 2i-6j+k. x(t)= 11 y(t) =…

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Q: Find a parametric form for the line through the point (8, –6, –3) and perpendicular to the plane 2x…

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Q: Find parametric equations for the intersection of the planes 2x + y − 3z = 0 and x + y = 1

A: Two planes lying in 3-Dimensional plane can intersect each other at any point and that point can lie…

Q: Find parametric equations for the line segment joining the points (9, 8) and (16, 11). O x=9+7t, y…

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Q: The parametric equation of the line through the origin that is parallel to the line given by x = t,…

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Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

A: Here we have to find the parametric equations of the curve C of intersection of the cylinder S:x2+y2…

Q: 4. Find the equation of the plane that passes through the point (5, –1,0), and is per- pendicular to…

A: Let's find.

Q: Find the point P of intersection between the line x(t) = (-3,-2, 1) + t (1, 1, -3) and the plane 4z…

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Q: Find the point at which the line given by the parametric equations below intersects the plane.…

A: Given a system of linear equations are, 2X + 4Y -3Z =-48.................(1) X = 10 +…

Q: d) Find the parametric equations for the line of intersection of the two planes.

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Q: The angle and the parametric equations for the intersect line between planes a + y = 1, and 2r+y-2z…

A: Given, x+y=1, 2x+y-2z=2 we know angle between two plane is…

Q: Complete the parametric equations for the line where the planes - 7x + y + 3z = 3 and 4x7y + z = 23…

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Q: 3. What is the parametric equation for the line through the point (1 ,2, 3) parallel to the x- axis?…

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Q: Find parametric equations for the line through the point, that is parallel to the given plane, and…

A: given point 0,2,2 given plane x+y+z=3 given line x=1+t,y=2-t,z=2t

Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

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Q: Find parametric equations for the line containing the points P(0,2,0) and Q(1,3,5).

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Q: Find the angle between the two planes x- 2y + z = 29, 2x + 3y – 2z = 6. And also find the parametric…

A: here we will find angle between two planes and parametric equation of plane's line of intersection,

Q: Given the curve of intersection of the x² + 4y² -z = 0 which is a paraboloid and the plane 2x - z =…

A: Solution:-

Q: Find parametric equations, in terms of t, of the line passing through (2, 2, 12) and parallel to the…

A: Given: The line is passing through 2,2,12. Also, it is parallel to the line: x=5-9ty=2z=4+t The…

Q: At which point will the plane 2x + 4y – 3z = -48 and the line given by the parametric equations x =…

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Q: Complete the parametric equations for the line where the planes - 7x + y + 3x = 3 and 4x7y + z = 23…

A: Given two planes -7x+y+3z=3 and 4x-7y+z=23

Q: State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Given: The equation of two planes are: V1 : x − y + z − 2 = 0, V2 : 2x + y + z − 4 = 0

Q: Find the parametric equations of the line segment through the origin and perpendicular to the plane…

A: Given: Given equation of the plane is x-2y+3z=5 We want to find the parametric equations of the line…

Q: What is the parametric equation for the line through the point (1,2,3) parallel to the y- axis? (a)…

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Q: Find parametric equations for the line in which the planes 3x - 6y -2z = 15 and 2x + y - 2z = 5…

A: Equation of plane - 1,3x-6y-2z = 15 Normal vector of plane 1 = n1 = 3,-6,-2…

Q: Q1: Two lines in space {x 1- 2t,y 2 +3t,z =-1+t} and {x = 1+t,y% 3+ 2t,z = -1+3t} find the angle…

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Q: Complete the parametric equations for the line where the planes 8x + 13y – z = 27 and 9x + 15y – 12z…

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Q: Complete the parametric equations of the line through the points (7,3,-5) and (0,6,1) x(t) = 7 - 7t…

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Q: The parametric equations r = 3 - t, y = 2t + 4, 0 <t < 2 describes motion along a certain line…

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Q: Find parametric equations of the line through (-2, –1, 3) that is parallel to 2i – 3j+k. x(t) = %3D…

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Q: Find the parametric equations for the line of intersection of the planes x+y-z = -20 and 9.x + 3y +…

A: Given planes, x+y-z=-20 and 9x+3y+z=16. The objective is to find the parametric equations for the…

Q: Find the symmetric and parametric equation of the line that is the intersection between the planes…

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Q: b) Find the area of the triangle with vertices P, Q, R. c)Write down parametric equations for the…

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Q: 22. Find (a) parametric equations for the line of intersection, and (b) the cosine of the angle…

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Q: 3. What is the parametric equation for the line through the point (1,2,3) parallel to the y - axis?…

A: The solution is given as follows

Q: Complete the parametric equations of the line through the point (-3,1,-4) and perpendicular to the…

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Q: Complete the parametric equations for the line where the planes -4x + 2y – 14z = – 32 and -x – y –…

A: Use parametric equation of tangent line

Q: Find the parametric equations for the line of intersection of the planes x+y+z= 3 and 2:z-3y = 6.…

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Q: Find the parametric equation for the line where the planes - 3y = 3 and -r - y+ 5z = - 9 intersect.…

A: The intersection of two plane is a line or the overlapping plane. Direction of the line is…

Q: Find the (perpendicular) distance from the line given by the parametric equations ¤(t) -2 – 2t y(t)…

A: Solution: The objective is to find the perpendicular distance

Q: The angle and the parametric equations for the intersect line between planes a+y = 1, and 2r +y - 2z…

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Q: Complete the parametric equations of the line through the point (8,6,-2) and perpendicular to the…

A: equation of line passing passing through the point 8,6,-2 and perpendicular to the plane , x-7y-z=-3

Q: Provide parametric equations for the line passing through the coordinates (1, −3, 2) and…

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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.