Find the point where the given line intersects the given plane x = 1-t, y = t, z = 1+t, z = 1- 2x +y

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: 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: 5. Determine the equation of the plane that contains the point (0,3,0) and the X = 1 line y = 2t z =…

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Q: 20. Find the point at which the line a = 1+ 2t, y = 4t, z = 2 –t intersects the plane r+y – 2z +1=…

A: Given that, equation of line:- x=2t, y=4t, z=2-t Equation of Plane:- x+y-2z+1=0

Q: (b) Find an equation of the plane that contains the line x = 1 + t, y = 2-t, z = 4 - 3t and is…

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Q: Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = 0.

A: Given Line is x=1+t,y=2t and z=-3t  And Given plane is x+y-z=0

Q: Find the intersection of the plane – 5x + 4y – 6z = – 267 and the line T(t) = (6, – 7,6)t + (1, – 7,…

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Q: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: Find the distance of point A(1,0,2) to the plane 3x+y+z=9?

A: Here we have to find the distance from the point A(1,0,2) to the plane 3x+y+z-9=0

Q: Find the distance from the line x = 2 + t, y = 1 + t, z = -(1/2) - (1/2)t to the plane x + 2y + 6z =…

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Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with .the xy-plane,…

A: In xy plane z = 0 = t - 3. Therefore t = 3 so the point of intersection is (-2,10,0). Similarly.

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

A: Given that  x = 2 − 2t,    y = 3t,    z = 1 + t;    x + 2y − z = 4 first we will substitute values…

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 distance between the parallel planes. x + y + z = 1 and x + y + z = 3

A: The distance between two parallel planes is the shortest distance between their surfaces. Distance…

Q: 24. The plane that contains the line x = 1 + t, y = 2 – t, z = 4 – 3t and is parallel to the plane…

A: To find out equation of plane first we change the equation of line in symmetrical form then find out…

Q: Find the equation of the plane that contains point P1(1,0,3) and orthogonal to line L1:(5t – 1,3 –…

A: Consider the line L1given by the vector form: L1:5t-1, 3-2t, t    :-1+5t, 3-2t, 0+t    :-1, 3, 0+5t,…

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: .) Find the plane which contains both lines: a. x = 1-4t, y = 1+2t, z = 2-2t b. x = -1+s, y = 2+s, z…

A: Since you posted here 3 questions,  I can answer only first one.  Please reupload remaining two…

Q: Find the point of intersection of the lines 2t + 1, y = -t+ 2, z = t+ 1 and x 2s + 2, y = s+3,z =…

A: Given lines are x=2t+1, y=-t+2, z=t+1x=2s+2, y=s+3, z=5s+6

Q: The line X=t, y+1=t, Z=t intersects the plane. x-2y+Z=2 at the point

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Q: Determine whether the plane x + y + z = 9 and the line x = t, y = -2t + 1, z = t + 2 are parallel,…

A: The given equation of line is in parametric form, x=ty=-2tz=t+2 Convert it into the cartesian form,…

Q: 2. Find an equation of the plane that contains the line r = 1 +t, y = 2 - t, z = 4 – 3t, and is…

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Q: Find the distance between the given point and the given plane. Point: (−1, 4, −2) Plane: x+2y+z=3

A: We can use distance formula to calculate the distance.

Q: 2. Find the plane that is orthogonal to the line : +1 = 431 = z and contains the point where l…

A: line parallel to the vector  V=⟨a,b,c⟩ passing through the point (x1,y1,z1) is given by the…

Q: Consider the line which passes through the point P(5, 2, -1), and which is parallel to the line x =…

A: Introduction: In three dimensional geometry, there are three fundamental planes referred to as the…

Q: / Find the distance from the line x 2 + 1, y 1 +1, z = -(1/2) - (1/2)t to the plane x + 2y + 6z 10.

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Q: Find the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y -…

A: We have to find the point at which the line intersects the given plane.

Q: The distance from the point P(1,2,3) to the plane x +y + z = 0 is

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Q: Find the plane containing the intersecting lines x = -1+t, y = 2+ t, z =1–t; -0 <t < o∞ | L2: x = 1…

A: Find the planes containing the intersecting lines: L1:x=-1+t,y=2+t,z=1-t for all…

Q: Find the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y –…

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Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3,…

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Q: Determine the point of intersection of the line and the plane. e:[x, y, z]= [3, 1, 2]+t[1, -4, -8]…

A: Finding the general point in the line substituting in the equation of a plane

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: Show that the line x = −1 + t, y = 3 + 2t, z = −t and the plane 2x −2y−2z + 3 = 0 are parallel, and…

A: Here we have to show that the given line,  x=-1+t, y=3+2z, z=-t and plane 2x-2y-2z+3=0 are parallel…

Q: Find the distance from the line x = 2 + 1, y = 1 + 1, z = -(1/2) – (1/2)t to the plane x + 2y + 6z =…

A: The equation of line: x=2+t,  y=1+t,  z=-12-12tTherefore:x-21=y-11=z+12-12 Equation of the plane is:…

Q: What is the symmetric equation of the line that is normal to the plane x + y + z = 9 at the point…

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Q: Find the general equation of the plane containing the point (2, –1,4) and normal to the line 2 = =…

A: As the line is normal to the plane, the DRs of the line and normal of plane is same.

Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with the xy-plane,…

A: Given, The line x = -2,  y = 4+2t ,  z = -3+t   We have to find the points of intersection of line…

Q: Find the general equation of the plane that contains the point (2, 0, 3) and the line x =−1+t, y =…

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Q: A normal equation of the plane that contains the line 1₁: (x, y, z) = (1, -1, 2) + t (9, 1, 3), t E…

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Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

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Q: Find the distance between the plane x+y +z = 3 and the line L= λ(1,0,-1).

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Q: What is the intersection of the plane x+2y+z=0 and the line (x,y,z) = (0,1,2)+ k(-1,1,2), kER?…

A: hello greetings from bartelby.i am here to help you.

Q: What is the intersection of the plane x+2y-z=0 and the line (x.y,z) = (2,2, - 3)+ k(4,–1,1), kER?…

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

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Q: Find the angle between the line 2 x+v3 : = z + 1 and the plane vZx + y + z – 2 = 0.

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Q: ind the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y –…

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Q: Find the point at which the line intersects the given plane. x = y − 1 = 3z;    4x − y + 3z = 11

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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.