Let L be the line whose symmetric equations are x-1=1=z+1. The equation of the plane through the point 9. P(2,3,-1) and orthogonal to L is x+9y+z=28 O x-9y+z=-26 9x+y+z=20 x+y+9z=-4 x+9y+z=30

Q: 2. Find the equation of the plane containing the lines L1: (x-2)/2 = (y+1)/-1 = z/3; L2: (x+1)/2 =…

A: Given that:L1: x-22=y+1-1=z3L2: x+12=y-1=z+23

Q: Find the point at which the line T(t) = (4, 1, 7) +t( – 5, – 7, – 4) intersects the yz plane.

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Q: 2-) Find the Symmetric form of the equation of the line of in tersection of the two Planes X- +Z =2,…

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Q: Q1// A :- Find an equation of the plane that passes through point (1,4,3) and contains the line…

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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…

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

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

A: Please refer the attached image for complete solution.

Q: Let L be a line which passes through the point (-5,0, 1) and is perpendicular to the plane x + 2y +…

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Q: Give the symmetric equations of the line l perpendicular to the plane T : 5x – 2y = z+4 and passing…

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Q: 1 2x 3y + z = 0 and 2 +t - 1 1

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Q: Find an equation of the plane containing the lines L1 and L2 in R3 L1: x = t ; y = -t ; z = t L2:…

A: We have to find equation of plane containg Line L1 and L2  -

Q: At what point does the line :LiX==€ 1=10+8€ 14. -2y t52 +16:0 10+3€ z=41+3€ intersect with the plane…

A: Question is based on 3d Geometry.

Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let L be a line which passes through the point (-5, 0, 1) and is perpendicular to the plane x + 2y +…

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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 a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

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Q: Let Q(0,-1,1) be a point in space and let u have the line L whose equation is L: 3- 3x = 1 – 3 y…

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Q: 10) Find the point of intersection of the lines L4:x = 1+ 2t, y = 2 + 3t, z = 3 + 4t and L2: x = 2 +…

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Q: Find the equation of a plane through the point (1, – 1, 6) and orthogonal to the line x(t) = 7 + 4t…

A: Required plane is orthogonal to the given line, say L: x(t)=7+4ty(t)=-3-4tz(t)=-1-6t also, the plane…

Q: Let L be the line x = t, y = -11 - 7t and z = -6 - 3t and let M be the line x = 1 +s, y = 2s and z =…

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Q: Find an equation of the plane containing the point (1,2,-2), and the line: x= 2t, y= 3-t, and z…

A: To find the equation of plane we need to find its normal vector. To find the normal vector, we…

Q: Find an equation of the plane. The plane that passes through the point (1, 2, 4) and contains the…

A: Topic = Vector correct answer e

Q: Let L be the line that passes through the point  (1,3,1 ) and orthogonal to the plane 3x-2y + 5z =…

A: In the question we have to find interacting points at which line and plane intersect.

Q: 1. Find the equation of the plane containing the lines L1 and L2 given below: z = 4t + 3 z = -4s – 1…

A: Given :L1:  x=2t+1, y=3t+2, z=4t+3L2 : x=s+2, y=2s+4, z=-4s-1

Q: Find the equation of the plane that passes through the point (−1, 2, 1) and contains the line formed…

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Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: If the line x=1+(a+2)t, y=1-bt, z=-1+(c-1)t and the plane -x+2y-323D0 are orthogonal to each other.…

A: Given: Ratio of lineA^=<a+2,-b,+c-1> Ratio of planeB^=<-1,2,-3>

Q: Find the intersection of the line r(t) = 3t + 2, 1, −7t and the plane 2x − 3y + z = 5.

A: r(t)=3t+2, 1, -7t and the plane 2x-3y+z=5

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

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Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane x + 2y +…

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Q: What is the equation of the plane containing point (3,0,4) and orthogonal to the line…

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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: Show that the line through two distinct points (x1, y1) and (x2, y2) in the plane has equation: | x…

A: Solution..

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

A: Find the vectors normal to the planes x + 2y - 2z = 5 and 5x - 2y - z = 0.

Q: Consider the two lines L: r = 2+3t, y =-2t, z = 1+4t and L2: x= 2- s, y = 2s, z = 1+3s. The equation…

A: We have two lines L1 and L2 . Equation of plane passing through any line is -  a(x-x1) +b(y-y1)…

Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane x + 2y +…

A: Here we find the equation of line L and also find the intersecting point of line and plane.

Q: If the line x=1+(a+2)t, y=1-bt, z=-1+(c-1)t and the plane -x+2y-3z=0 are orthogonal to each other.…

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Q: 2) Find the symmetric equation of the line containing the point (1, 2, 1) and perpendicular to the…

A: consider the direction ratio of line  contaning the point ( 1, 2 ,1 )  is  l , m, n

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

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Q: Find an equation of the plane that passes through the point (1,1,2) and contains the line x=3t, y=1,…

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

A: The line L is perpendicular to the plane, x+2y+4z = 0 Hence the direction ratios of the line L is…

Q: Let L be a line which passes through the point (-3, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Find the point at which the line intersects the given plane. x = 3 - 3t, y = 4t, z = 1 + t; x + 2y -…

A: Given line ,x=3-3ty=4tz=1+t   -1and plane , x+2y-z=6

Q: Find the equation of the plane passing through the point P(1,-1,2) and parallel to the lines =Dz and…

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Q: let L be the line whose symmetric equations are x-1=(y-1)/10=z+1. the equation of the plane through…

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

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Q: At what point does the line r(t) = (6- 3t)i + (-2 + 2t)j + (-1- 3t)k intersect the yz-plane %3D O a.…

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

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.