onsider the two lines in IR" given by: x -1 y- 2 z x +1 y m: z+3 a A. For which values of a do the lines intersect? B. For a value of a as above, give the general equation of the plane spanned by the lines. C. Find a line on the above plane except I, m. Express using parametric equations.

Q: Question Eliminate the parameter in the parametric equations x(t) = V/t – 1 and y(t) = -8t + 6 to…

A: Given: xt=t-1 and yt=-8t+6 To find: eliminate the parameter t and then obtain the cartesian…

Q: pair of parametr quations is given. x = e4t y = et (a) Sketch the curve represented by the…

A:

Q: DISCOVER: Intersection of a Line and a Plane A line has parametric equations x = 2 +1 y = 3t := 5 -1…

A: Given parametric equation of the line is , x=2+t , y=3t , z=5-tand the equaation of the plane is…

Q: In the following exercise eliminate the parameter t. Then use the rectangular equation to sketch the…

A:

Q: Part A Find the parametric equations of the line of intersection of the following planes: T1: 5x +…

A: Find the point of parametric equation of the line of intersection, and angle between two planes

Q: (a) Find parametric equations for the intersection of the planes 2x + y−z = 3and x + 2y + z = 3.(b)…

A:

Q: Find a set of parametric equations for the line passing through the point (7, 0, 1) that is parallel…

A:

Q: ketch the curve represented by the parametric equations (indicate the orientation of the curve), and…

A: The parametric equations are x=t ............. (1)  y=t-7 ...........(2)

Q: 35. DISCOVER: Intersection of a Line and a Plane A line has parametric equations y = 3t 2= 5 - 1 x =…

A: Given :   We have given parametric equations of the line                 x = 2+t           y = 3t…

Q: Consider the following planes. 3x + 6y-z = 126 x - 12y + 2z = 0 (a) Find the angle between the two…

A:

Q: a) | Find the parametric and symmetric equations of the line L which is the intersection of the…

A:

Q: Q1) Write the parametric equations of the line of intersection of the planes 2x-y+z 5 Note: Consider…

A:

Q: Consider two non-parallel lines L1 and L2 in R2 with the following parametric equations: (3,6) +…

A: Given : L1 = (3, 6) + s(3, -4) and                   L2 = (-4, -6) + t(2, -4)

Q: B.Plot the (x, y) pairs in the table and the complete parametric curve, indicating the positive…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

A: We have to find the parametric equation of line which is passes throgh the given point and the…

Q: a) Find the parametric equations for the line tangent to the curve of intersection of surfaces at…

A: To find the parametric equation of the line tangent to the…

Q: Eliminate the parameter and graph the plane curve represented by the parametric equations. Use…

A: The parametric equation is x=2t-1 and y=1-t , -∞<t<∞

Q: da set of parametric equations for the tangent line to the curve of intersection of the surfaces at…

A:

Q: Find a set of parametric equations for the line passing through the point  (2, 0, 5)  that is…

A:

Q: (a) Find parametric equations for the line through  (4, 5, 4) that is perpendicular to the plane x −…

A: Parametric equation of a line passing through (x1, y1, z1) and perpendicular to the plane ax + by +…

Q: Find a parametric description of the line segment from the point P to the point Q. P(2,2), Q(22, -…

A:

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

A: This question is related to equation of straight line and plane, we will solve it using given…

Q: a(t) Write the Cartesian equation of the line given by the parametric equations < y(t) 1- 9t -1+t.…

A:

Q: X = 1 + 6t y = 2 + 4t, t ER z = 2t A line is defined by the parametric equation L : If the point (a,…

A:

Q: Question If x(t) = -2sint and y(t) = 3cos²t, eliminate the parameter to write the parametric…

A:

Q: Line l is given by the parametric equations: x = 1-2t  y = -2+4t z = 4+5t Determine the equation…

A:

Q: Question If x(t) = –2t – 3 and y(t) = -8t + 3, eliminate the parameter to write the parametric…

A: Given that:                              x = -2t - 3 Or,                        t=x+3-2…

Q: (b) Find a set of parametric equations for the line of intersection of the planes. (Use t for the…

A:

Q: Find a set of parametric equations for the line passing through the point (2, 0, 4) that is parallel…

A: To find a set of parametric equations for the line passing through the point 2, 0, 4 that is…

Q: Eliminate the parameter tto find a Cartesian equation in the form æ = f(y) for: Į ¤(t) = - 4t² I…

A:

Q: Čonsider the following planes. 5х — Зу + z %3 2, Зх + у - 5z %3D 4 Find parametric equations for the…

A:

Q: (a) Find parametric equations for the line through (4, 1, 4) that is perpendicular to the plane x -…

A: Topic- plane and equation

Q: NIM Let line l: x = = and point P(1,0,1). 2 Find the parametric equations of the line parallel to…

A:

Q: 3.) the a. Find the distance between point and the line given by the set of parametric equations. (…

A:

Q: (a) Find parametric equations for the line through (5, 2, 6) that is perpendicular to the plane x-y…

A:

Q: y Let line l: x == and point P(1,0,1). 2 3 ● Find the parametric equations of the line parallel to…

A:

Q: (a) Find parametric equations for the line through (3, 5, 8) that is perpendicular to the plane x -…

A:

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

A:

Q: nin m Find the distance between the point and the line given by the set of parametric equations.…

A: This question is based on 3-d line.

Q: Find parametric equations for the line through (- 4,7,6) parallel to the y-axis. .... . Choose the…

A:

Q: Find parametric equations for the path of a particle that moves along the circle  x2 + (y − 1)2 = 4…

A: Given the equation of the circle is x2+y-12=4

Q: onsider the following planes. x + y + z = 3, x+ 6y + 6z = 3 (a) Find parametric equations for the…

A:

Q: Eliminate the parameter and graph the plane curve represented by the parametric equations x = t2, y…

A: x=t2,  y=t-1 Consider, y=t-1⇒t=y+1 Now put t=y+1 in x=t2, we get ⇒x=y+12⇒x=y2+2y+1⇒y2+2y-x+1=0

Q: 5 X =- (x+y-z=2 and b: 15b. Given the non-intersecting lines a: y = k keR x-2y+z 1 2 --= Z - k…

A: Consider the given lines: a:x+y-z=2x-2y+z=1 solving the equations of the planes using the matrix…

Q: c) The equation of a second plane that contains the point (2, 0, 4) and has normal vector <2, -4,…

A:

Q: Question 2 (a) Let S1 be the plane which contain lines L, and L2 whose parametric equations are…

A:

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.