2. Find the equation of the plane containing the lines L1: (x-2)/2 = (y+1)/-1 = z/3; L2: (x+1)/2 = y/-1 = (z+2)/3. That is L1 and L2 are parallel lines.

Q: 1. Find the equation of the plane that contains the point (-1, 1, 2) and the line given by x=1-t,…

A: This question is based on 3d geometry.

Q: The point of intersection between the line t with the plane 2x + 3y +5z = 31 is

A: Given line ,x-1-4=y-13=z5=tTherefore any point on the line is of the form (1-4t,1+3t,5t)Put this…

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

A:

Q: The equation of the plane that passes by P(2,0, -1) and that is perpendicular to the line x-5 2-y Z…

A: The plane passes by P2,0,-1 and that is perpendicular to the line x-5-2=2-y4=z-23

Q: Find the point where the line x = 8/3+ 2t, y = -2t, z = 1 + t intersects the plane 3x + 2y + 6z = 6.

A:

Q: find the plane containing the intersecting lines.  L1: x = t, y = 3 - 3t, z = -2 - t; -inf < t…

A: This question is taken from the planes in which we have to find the plane equation. We can write the…

Q: Consider the two lines Lı : x = 2- 3t, y = -1+ 2t, z = and L2: r = 2+ s, y = -1- 3s, z = that…

A: We will find out the required equation of plane

Q: Show that the lines determined byr 1(t) = < 7, 3 − 4t, 2 + 6t> andr 2(t) = <6 − t, 3 + 8t,…

A: Given: r1(t)=7,3-4t,2+6t r2(t)=6-t,3+8t,9-5t For r1. x-7=y-3-4=z-26=t For r2. x-6-1=y-38=z-9-5=t…

Q: The line : X - 3t, y = 1 - 2t, z = 2 - t is perpendicular to the plane: X - y - z = 1.[g]

A: Given that equation of line x=-3t ,y=1-2t ,z=2-t and equation of plane x-y-z=1To chaque the line and…

Q: Determine whether the line L : x = 3 – 4t, y= 5+2t, z = 5 + 4t, - is parallel to the plane x - y +…

A:

Q: At what point does the line: L: x=-1, y= 10 + 31, z= 4 +3t im plane 1:x- 2y + 5z + 16 = 0?

A:

Q: Determine the equation of the plane that contains the lines Li and L2. L: x = 3- t, L2: x = 8 +2 s,…

A:

Q: Find the plane containing the intersecting lines L1: x = -1+t, y= 2+t, z = 1 – t; L2: x = 1 – 4s,…

A: The given intersecting lines are  L1: x=-1+t,y=2+t,z=1-t; -∞<t<∞L2: x=1-4s,y=1+2s,z=2-2s;…

Q: Find the point at which the line (-3, 3, 0) + t(-2, –3, –2) intersects the plane -2x – y + 3z = 5.

A:

Q: Find the equation of the line that contains the point (1,–1, 2) and is perpendicular to the plane 2x…

A:

Q: Find the point where the line x=8+2t, y3-2t,z=1+t intersects the plane 3x+2y+6z36.

A:

Q: What is the real number a that makes the line 2 -1 y-12 z-7 a -2 3 parallel to the plane z -y - 2z=…

A:

Q: Find all planes in R^3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

A: To find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.…

Q: Find the point of intersection of the line x-9 = - 5t, y +1= -t, and the plane 2x – 3y + 4z + 7 =0-…

A:

Q: 4. Write the equation of the plane parallel to the z-axis, with xy-trace x + y - 2 = 0.

A: Write the equation of the plane parallel to z axis, with xy trace x+y-2=0.

Q: Find an equation of the plane containing the lines given by 1-x = y = z+ 1 2 and * = y – 1 = z - 2…

A: From the given problem:, the plane containing lines are: 1-x2=y=z+1andx+1-2=y-1=z-2 So we can simply…

Q: Find the equation of the plane perpendicular to the line x 2t, y = 6 - t, z = 4+t and containing the…

A:

Q: Suppose we need to find an equation of the plane that passes through the line of intersection of the…

A: Since, we know that equation of a plane passing through the intersection of planes P and Q is given…

Q: If the line L: X = 3 + 2t , Y= 2t , Z=t intersects the plane X+ 3y Z -4 in a point P. The…

A:

Q: Find the Polnt otintersectton of the lines: l,: x = 2+t, y =3+2t,z z 4 +3t X = S+ 2, y= 2S+4, 2=…

A: Here we will find the point of intersection of given lines,

Q: Find the point at which the line (4, –1, 4) + t(4, 2, 3) intersects the plane 4x 5y + z = 88.

A:

Q: Consider the lines x – 4 l2 : 4 - 1 l1: x= 4 – 3t, y = 2t, z = 1 + 5t , %3D 2 (b) Find an equation…

A: Given that:                        Two lines are: l1: x=4-3t, y=2t, z=1+5t,  l2:x-44=y1=z-12

Q: Find the distance between the given parallel planes. 2x - 3y + z = 8, 4x - 6y + 2z = 1

A: The solution are next step

Q: Find the point of intersection between the line r(t) = + t and the plane 4x + 5y + 3z = 5. o a. (…

A:

Q: 4. Find the equation of the plane that contains the intersecting lines a = 4 +t1, y = 2t1, z =1-3t…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two…

A:

Q: 2) Find the equation of the plane that is orthogonal to the planes 3x-2y-2z=1 and x-3y-10z = 4 and…

A: Given: The equation of two planes 3x-2y-2z=1 and x-3y-10z=4 and the equation of one line…

Q: 5. Find the equation of the plane that passes through the point (6,0,-2) and contains the line X =…

A:

Q: Find the equation of the line containing the point (1, 3, −2) that is parallel to both of the planes…

A:

Q: 16- Find the equation of the plane that contains the line = 5 - z, and the %3D point P( 0,5,2).

A:

Q: Find the distance between the given parallel planes. 2x - 4y + z = 8, 4x - 8y + 2z = 3

A:

Q: х —7 у-5 z-1 L: 4 -,P: 2x + y – 7z +1 = 0 6. 3

A: Given Data: Line: x-74=y-53=z-16 Plane: 2x+y-7z+1=0 Let t is a constant variable for line,…

Q: Find a line equation through the point P(1,2,3) and parallel to the line of intersection of the…

A: Planes as:                       2x+y-z=3x+2y+z=2;   The given point as:                        (1,…

Q: Show that the line in which the planes x + 2y – 2z = 5 and 5x – 2y - z = 0 %3D intersect is parallel…

A:

Q: what is the equation of the plane perpendicular to the intersection line of the x-2y+2z= 3  and…

A:

Q: 1. Determine the point of intersection of the line and the plane if it exists. π: 7x+y+ 5z = 0 x-4…

A:

Q: find the point in which the line meets the plane x = 2, y = 3 + 2t, z = -2 - 2t; 6x + 3y - 4z = -12

A: The equation of plane is 6x + 3y - 4z = -12. The coordinates of the line is x = 2, y = 3 + 2t, z =…

Q: Find an equation for the plane containing the two (parallel) lines v, = (0, 1, –4) + t(1, 3, –5) and…

A: Solution: The objective is to find an equation for the plane containing the two parallel lines

Q: If the line L: X = 3 + 2t , Y= 2t , Z = t intersects the plane X+ 3y - Z =-4 in a point P. The…

A:

Q: . Find the equation of the line containing the point (1,3, –2) that is parallel to both of the…

A:

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

A:

Q: Does the line r(t) = intersect the plane 5x - 2y - z = 21 and if so, where?

A: