State whether the following pairs of planes intersect. If the planes intersect, determine the parametric equations of their line of intersection. V1= x − y + z − 2 = 0, V2= 2x + y + z − 4 = 0.

Q: In the given equation as  follws , find a set of parametric equations forthe rectangular equation…

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

Q: For the parametric equations: = 31e-4t and y = 32et %3D da

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Q: Find the parametric equation of the line ( x-3, y+6 )•( 2,-3 ) = 0

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Q: Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 42² = 4…

A: To find: Parametric equation of the Intersections of the curves  4x2+y2+4z2=4 and y2=x2+2z2.

Q: Complete the parametric equations for the line where the planes – 4

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Q: Find two different sets of parametric equations for the rectangular equation   y = 4/(x − 1)

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Q: Given the parametric equations, x = 3/t and y = t - 2, eliminate the parameter. y = --2 y = +2 y =…

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Q: Eliminate the parameter in the parametric equations x(t) = -6t + 8 and y(t) the equations. = 30t –…

A: givenx=-6t+8....................(i)and y=30t-10...................(ii)x=-6t+86t=8-xt=8-x6

Q: Eliminate the parameter to write the parametric equations as a Cartesian equation. If x(t) = 3t – 2,…

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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 the parametric equations for the line in which the planes -4x +y+3= = 5 and 2x+y+ = 3…

A: Given that:-4x+y+3z=5    .............(1)2x+y+z=3          ..............(2)

Q: Complete the parametric equations of the line through the points (4,-8,1) and (-7,2,-2) x(t) = 4 –…

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Q: Find two different pairs of parametric equations for y = - 2x + 4.

A: The given equation is: y=-2x+4 Consider, x=t Then, y=-2t+4

Q: The parametric equations for x3+y/3-4 , when 0s0<2n are:

A: See the attachment

Q: 1: Find the angle between the planes 3x - 6y + 4z 3 and 2x - 2y +z = 4 then find the parametric…

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Q: i) Eliminate the parameter for the given set of parametric equations, sketch the graph of the…

A: Given: x=6-7 e-2t &amp; y=4+3 e-2t To eliminate the parameter t &amp; to sketch the graph of…

Q: Given the parametric equations, x = 2t + 5 and y = 3t2 - 1, find the point on the graph at time, t =…

A: We can find the point as below

Q: Complete the parametric equations of the line through the point (-2,-4,-8) and perpendicular to the…

A: Given: Equation of plane x-3y-5z=2 Point (-2,-4,-8)

Q: Cannot solve

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Q: If æ (t) = -2sin t and y(t) = 3cos²t, eliminate the parameter to write the parametric equations as a…

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Q: Find two different sets of parametric equations for the rectangular equation y = x2 + 4.

A: To find the set of parametric equations

Q: Write the parametric equations x = 2t – t°, y = 4 – 2t - in the given Cartesian form.

A: We are given the equation of the function in parametric form and we need to find the cartesian form…

Q: x = 12 + 3 y = 2t [-2, 2]

A: Substitute t value

Q: Q2:- Find the parametric equations for the following Cartesian equations. 1) x=(/y² + 4 + 2) 2) 4x2…

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

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Q: Eliminate the parameter in the parametric equations æ(t) = /t – 1 and y(t) = -8t + 6 to find a…

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Q: Find two different sets of parametric equations for the rectangular equation y = x2 - 3.

A: Find two different sets of parametric equations for the rectangular equation y = x2 - 3

Q: Find parametric equations for the line described below. The line through the point P(3, 2, 4) and…

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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: (i) Find the acute angle (in degrees) between the following two planes:  8x+6y+12z=24 and…

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Q: Complete the parametric equations of the line through the point (3,-7,-2) and perpendicular to the…

A: Given that, the equation of the plane is     -3x-y+z=2  and the point (3,-7,-2) The direction vector…

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: Eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x= -2 t+6 y=…

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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: Write the parametric equations x=2sinθ,y=9cosθ,0≤θ≤πx=2sin⁡θ,y=9cos⁡θ,0≤θ≤π in the given…

A: Given information: The parametric equations are x=2sinθ            y=9cosθ             Can be…

Q: The position of an object at time tis given by the parametric equations

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Q: If not, find a parametric equation of the line of intersection of the two planes. Find, correct to…

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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 two different sets of parametric equations for the rectangular equation  y = x2

A: y=x2 Let x=3t, then y=3t2=9t2 Now let x=4t, then  y=4t2=16t2

Q: Find two different sets of parametric equations for the rectangular equation  y = 4x + 1, t = −1 at…

A: Given equation is y=4x+1, t=-1 and the point is (-2,-7).

Q: Find a set of parametric equations for the rectangular equation that s y = 2x – 3, t = 0 at the…

A: let x = t + a put all the given points to find out the value if a x = 4 and t = 0 4 = 0 + a a = 4 so…

Q: Find the parametric equation of the line through (1, 0, -2) and parallel to the line % (x – 4) = ½…

A: according to our guideline we are supposed to answer only the first question if you want any…

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.