Consider these lines, where s,t, E R 11: [x, y, z] = [2, 1, -4] + t[1, 3, 1] 12: [x, y, z] = [1, k, –3] + s[-1,1, -2] Determine the value of k so that /1 and 12 lie on the same plane.

Q: The equation of the plane that contains the point (1, 2, 3) and the line x = 4t, y = t, z = t is…

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Q: Find a function r(t) that describes the line through P(3,4,5) that is orthogonal to the plane 2x-z=4

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Q: Let P(x1, y1) and Q(x2, y2) be two points in the plane. Prove that the equation of the line through…

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Q: Find the line of intersection of the planes z + 2y – z = 1 and z + y + z = 1. Lütfen birini seçin:…

A: Given equation of plane is x+2y−z=1 and x+y+z=1. We have to find the line intersecting of the plane…

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: 10. Suppose that II1 and II2 are parallel planes in R’, given by: Il : ajx + bịy + C1z = di, and II2…

A: Given two plane which are parallel  Π1:a1x+b1y+c1z-d1,  Π2:a2x+b2y+c2z-d2 and another plane is…

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: Consider the two planes, T1: X = 4 – 2s + 3t - y = 1 +s + 2t z = 3 + 4s -t; s, t eR T2 : [x, y, z] =…

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Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the plane through U, V, and W, expressed in…

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Q: Let T, denote the plane parallel to the xz-plane through the point (1, 2, 3). Let n2 denote the…

A: To solve this problem first of we find the equation of the plane π1 and π2 in standard form and then…

Q: Let the π1 plans be: mx − ny + z = 2 and π2: nx − m y + nz =4, with m, n ∈ R. a) Determine m and n…

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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: 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: Let the vector ü = (k,5,-1) and v=(2k,k,3) are perpendicular in R, find the value of k that related…

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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: Determine the distance between: the pa rallel line x-a++ X - 3+S+t t9= 5-t,tER and the…

A: Given line is                                                     x=2+ty=5-tz=-4 point on the line…

Q: Which of the following planes is normal to the line given as: x = 2t + 3, y = 5t - 7, z = t - 4 O a.…

A: This question is based on dot product.

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

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Q: If possible, determine the vector, parametric,symmetrical and reduced line r that: a) passes…

A: Given the lines S1:t·1,2,3, t∈ℝ and S2:y=x+2, z=x. To find a line L passing through the point P1,1,1…

Q: Show that the rank of the linear mapping 7.32. Bar Y3= 301 +302 y = 201 +20203, 31-02-203 1 V2 is…

A: To prove that the rank of the matrix (representing the given linear transformation ) is 2 and to…

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: Let L,:x = 3t +5, y = 2+t, z = 2+ 3t L2:x =t - 2, y = t + 1, z = 1-2t Two lines in space and let's…

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Q: Find an equation of the plane through (– 1, 3, –4) that is perpendicular to the planes 8x – y + z =…

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Q: Find an equation for the line of intersection of the planes bx+z=0, by+ cz =b, where b,c are real…

A: the equation of the line of intersection pf the given planes ...

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: Prove that the intersection line of the planes P₁: 2x -y - 2z = 0 and P₂:x-2y+z = 0 is parallel to…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

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: Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0)…

A: Given equation of plane ax+by+cz+d=0. The plane ax+by+cz+d=0 will divide the xyz space into two…

Q: Let L, be the line through the points (1,2,6) and (2,4,8). And let L2 be the line of intersection of…

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Q: Find the line of intersection of the planes x- y- 2z 1 and a +y+z=-1. Lütfen birini seçin: a.L : x =…

A: Given equation of plane is x−y−2z=1 and x+y+z=−1. We have to find the line of intersection of the…

Q: The pole holding up one end of a volleyball net is perpendicular to the plane containing the points…

A: Paragraph proof: You are given that VW⊥WX and VW⊥WY,which implies that ∠VWX   and   ∠ VWY are right…

Q: Let the π1 plans be: mx − n y + z = 2e π2: nx − m y + nz = 4, with m, n ∈ R. a) Determine m and n so…

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

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Q: Select all lines that are parallel to the plane x+y+z%= 3. OF(t) = (1,1, 1) + t(1, 1, –2) OF(t) =…

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Q: Let L be a line which passes through the point (-6,0, 1) and is perpendicular to the plane x + 2y…

A: Direction ratio of Line is < 1,2,6> Write equation of straight line and solve it with plane to…

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: Given the following two lines: D:: (x,y,z) = (2,0, 0) + k (0,3,0) and Dz: (x,y,2) = (2,0,2) +k…

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Q: Given two lines L1 : x =t+1, y = 3t + 1, z = 2t – 1, and L2 : x = 2t – 2, y = 2t + 3, z =t +1,…

A: The given lines are L1:x=t+1,y=3t+1,z=2t-1L2:x=2t-2, y=2t+3, z=t+1 and a plane H is parallel to both…

Q: Let L be a line satisfying the following two conditions: ) L passes through the point (6,2,3). ii) L…

A: given : line passes through the point (6,2,3)          line perpendicular to plane 5x+9y+5z=-3 since…

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: 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 <2, m, m> . The direction…

Q: Consider a point Q(x1, y1, z1) and a line L given by the vector equation r = r0 +tv,where r0 =…

A: First obtain a, where a is the distance between R0 and Q.

Q: Choose a set S of four distinct points in R3 such that aff S is the plane 2x1 + x2 – 3x3 12. Justify…

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Q: Let L1 be the line through the points (1,2,6) and (2,4,8). And let L2 be the line of intersection of…

A: We have to find the distance between line L1 and L2.

Q: The plane a is determined by the points A = (1,0, 1), B = (2, –1,0), and C = (1, 1, –2). L, is the…

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Q: Determine an equation of the form Ax t t Cz + D=O By for the plane that contains the line (x,y,2)=…

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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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Q: Consider in R° the following planes: p:2x+y-3z=-18. 6:x-3y+4z=4. Let ë be a plane perpendicular to…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.