12) Find the intersection of the plane: x – z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

Q: Choose a set S of three points such that aff S is the plane in R3 whose equation is x3 = 5. Justify…

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Q: B. Show that line is parallel to plane x-2y + z 6

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Q: Find the equation of the plane containing the line of intersection of the two planes z+y+z+5=0 and…

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Q: 25. Find the intersection of the line [x, y, z] 2х — 4у + 7z —26 %3D 0. [1,4, – 2] + t[1, – 1,3] and…

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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: Locate the point of intersection of the plane 2x + y−z = 0 and the line through (3, 1, 0) that is…

A: Our Aim is to locate the point of intersection of the plane 2x+y-z and theline through (3,1,0) that…

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: (A) Determine the plane that contain the point A(2,5,1) and the line L, t=x-2, 3t =y-1, t=z+1

A: The equation of the line L given in the parametric form, that is, Thus, the above equation of the…

Q: Where does the line through (1,0, 1) and (4,– 2,2) intersect the plane x+y+z = 6?

A: It can be assumed that the vector for the coordinate 1,0,1 is 1,0,1 and the vector for the…

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: (6) Where does the line through (1,0, 1) and (4, -2, 2) intersect the plane r+y+ z = 6?

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Q: 3. Find the plane determined by the intersecting lines L: x = -1+t, y = 2+t, z = 1- t; L2: x = 1 -…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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

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Q: Is the line x = 4 + 2t, y =-t , z=-4t - 1 parallel to the plane 3x + 2y + z = 7 ?

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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: Consider the equation of plane x+2y+z=0 and the equation of line x,y,z=0,1,2+k-1,1,2. Find the…

Q: Find the plane that contains the point (0, 1, 2) and the line x = 1- t,y = 2 + t,z = 4 + 3t.

A: Here I am attaching image so that you understand each and every step.

Q: (A) Find the Distance between the point (x.y.z) and the plane 3x+2y+6z = 6 If the plane meet with…

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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: 6. Find the intersection of the line I and the plane r. 1:F = (4,-1,4) + t(5,-2,3) T: 2x+5y+z+2=0

A: answer is in next step

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: 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: The line x=4+2t, y=-t, z=-1-4t is parallel to the plane 3x+2y+z=7 FO

A: Direction cosine vector of the line is: L=2,-1,-4 and normal vector to the plane is N=3,2,1.

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

A: Substitute the line equation in the plane equation

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: Find the distance between two lines (L1: x=3t-1, y=t+6, z=2t+3 and L2: x=2t+6, y=2t+11, z=-t+3)…

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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: 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: 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: 4. Find an equation for the plane in R spanned by the points (1, 5, 1) and (1,4, 2).

A: Given v1 = (1 , 5 , 1)v2 = (1 , 4 , 2) Let xyz be a point in spanv1 , v2 , so there exist m , n…

Q: Find the point of intersection of the line x = 2 − 3t y = 4 + 2t −∞ &lt; t &lt; ∞, z = 3 − 5t, and…

A: x=2-3ty=4+2tz=3-5tand the plane 2x+3y+4z+8=0

Q: The intersection point of the line whose equation is (x+2y+z=1),(x+y+2z=-1) with the xz plane is: O…

A: Here the two equation are: x+2y+z=1x+y+2z=-1

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

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Q: Find the distances (a) Between l1 = (2+ 2t, –1+t, -3t) and l2 = (4, -5 – 3t, 1+ 4t) (b) Between the…

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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 +…

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

Q: (A) Find the Distance between the point (x.y.z) and the plane 3x+2y+6z = 6 8 If the plane meet with…

A: As per the company policy i can answer only first question for you, More than that leads me towards…

Q: Find m, n ∈  R so that the line r X: (n, 2,0) + λ (2, m, m) is contained in a plane π: x -3y + z = 1

A: The direction cosines of the line, r(x)= (n, 2,0) + λ (2, m, m) are &lt;2, m, m&gt; . The direction…

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: 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: 4. Find the point of intersection of the plane z= 4 and the line L={ (x, y, z) | x= 4 + 3t, y=-1-2t,…

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Q: Find the point at which the line intersects the given plane. x = 4 - t, y = 5 + t, z = 3t; x - y +…

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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: 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: Let P be the plane with equation −x+2y−2z = 3. Find four distinct points on P at distance 3√10 to…

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