Q2/ Let Li be the line through the points (1, 2, 6) and (2, 4, 8). Let L2 be the line of intersection of the planes 7 and 72, where m is the plane x - y + 2z + 1 = 0 and 72 is the plane through the points (3, 2, – 1), (0, 0, 1), and (1, 2, 1). Calculate the distance between Li and L2. |

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

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

A: x = 4 − t,  y = 2 + t,  z = 3t;    x − y + 5z = 15 We need to find the point at which the line…

Q: A perpendicular line is drawn from point P(1,2,1) to the plane -2x + 4z = 4 and meets the plane at…

A: Given that a perpendicular line is drawn from point P(1,2,1) to the plane -2x+4z=4 and meete the…

Q: 2. The plane containing the point (-8, 3, 7) and parallel to the plane given by 4x+8y-2z=45.

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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,…

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Q: Determine the distance from point P(–2, –1, 1) to the plane [x, y, z] = [4, –1, 6] + t[1, 6, 3] +…

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Q: Choose the line which is completely on the plane 2x+3y-4z= 12. Select one: x-1+3t, y= 1+3t, z 2+2t,…

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Q: 6. Determine the distance from the point (2, -1, 5) to the plane 3x - 3y + 5z = 8.

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane given…

A: Given problem:- Find the point of intersection of the line through (1,-3, 1) and (3,-12, 6), and 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: Determine the equation of the plane containing the points (3, 1, 4) and (2,7, 1) and is perpen-…

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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,…

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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: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, - 1, 2) is parallel | to the line x=…

A: Given that points are (2,1,-1), (0,-2,0) and (1,-1,2) The parametric equation is,…

Q: Find the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10.

A: Given,           The distance between the point 2,-4,3 and the plane 5x-2y+z=10.We know that,…

Q: A perpendicular line is drawn from point P(1,2,1) to the plane -2x+ 4z 8 and meets the plane at…

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Q: Find the point on the plane x−3 y+3 z =−8 that is closest to the point (−2,−2,0) .

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Q: The lineL: x = 3 + 2t, y = 2t, z = tintersects the plane x + 3y - z = -4 in a point P. Find the…

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Q: Where does the line through (1, 0, 1) and (4, −3, 3) intersect the plane x + y + z = 6?   (x, y,…

A: Given points are Given Plane is

Q: Find an equation of the plane whose points are equidistant from (6, -5, 3) and (7,5, 5). 13x + 8z –…

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Q: Find the distance from the point (-2, 1, 4) to the a. plane x = 3 b. plane y =-5 c. plane z =-1

A: Given:The point (-2, 1, 4).Formula:The distance between a point (x1, y1, z1) and the plane  is,

Q: Find the distance between the point (-1,–1,2) and the plane 2.x+5y-6z =4

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Q: Locate the point of intersection of the plane 2x + y - z = 0 and the line through (4,2,0) that is…

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given…

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Q: The plane through the points (2, 1, –1), (0, –2, 0), and (1, – 1, 2) is parallel to the line x=1-t,…

A: Equation of plane passing through x1, y1, x2, y2, x3, y3 is given by,…

Q: Find the point of intersection of the line through (1, -5, 1) and (5,-12, 6), and the plane given by…

A: we know that equation of line which passes through two pointsx1,y1,z1,x2,y2,z2 is given by…

Q: int at which the line ⟨4,−1,−5⟩+t⟨−3,3,2⟩⟨4,−1,−5⟩+t⟨−3,3,2⟩ intersects the plane…

A: Given the line 4,-1,-5+t-3,3,2  intersects the plane -x+y+z=18.

Q: Find the distance between the point (2, 8, 4) and the plane 2x + y + z = 5.

A: we have to find the distance between the point (2,8,4) and the plane 2x+y+z=5. as we know that the…

Q: Find the distance from the point (2,-3,5) to the plane passes through the points (1,0,-3), (3,4,-6)…

A: (b) Given point P2,−3,5 and a plane passes through the points 1,0,−3, 3,4,−6 We have to find the…

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: Derermine the pointof intersection of the linel:- [-6,9,-1]+t[-a,3 ,1], t ER, and the plane, TT-x +…

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

A: Given x=-2, y=4+2t, z=-3+tfor finding intersection with xy-plane , set z-coordinate…

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane given…

A: Given the point (1,-3,1) and (3,-12,6) and the plane x-y+z=6

Q: Find the point of intersection of the line through (1, -5, 1) and (5, -12, 6), and the plane given…

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Q: Find the distance between (1,-2, - 1)and the plane through the points (1, 2, 3)and (3 , 2, 1)and…

A: Given information: The plane passes through the points (1, 2, 3) and (3 , 2, 1) and perpendicular to…

Q: Find a plane containing the point (5,8,8) and the line of intersection of the planes -4x 4y+ 6z = 74…

A: We have to find the equation of plane containing the points 5,8,8 and the line of intersection of…

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

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given…

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Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, -1, 2) is parallel to the line x 1-t,…

A: equation of plane for non collinear points , x-x1y-y1z-z1x2-x1y2-y1z2-z1x3-x1y3-y1z3-z1 we will use…

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: Determine the distance from point P(-2, –1, 1) to the plane [x, y, z] = [4, –1, 6] + t[1, 6, 3] +…

A: Parametric equation of a plane is: x,y, z=p+at+bs where a and b are the vectors parallel to the…

Q: Find the points of intersection of the line 6. = y+3= z 4 with the plane I+ 3y + 2z – 6 = 0. ОА(-10,…

A: We will solve the following.

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

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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: Find the point of intersection of the lines x t, y = -t + 2, z = t + 1, and x 2s + 2, y s + 3, z 5s…

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Q: Find a plane through the point Po(2, 1, -1) and perpendicular to the line of intersection of the…

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -8, 4), and the plane given by…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.