Find the plane containing the intersecting lines: L1: x = -1 + t, y = 2 + t, z = 1 - t; -∞< t < ∞ L2: x = 1 - 4s, y = 1 + 2s, z = 2 - 2s; -∞< s < ∞

Q: 2:- find the line of interSection o f the plane -2x + 73 - 2324 given by 3x t6y-52=-3 f the plane

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Q: Find the plane determined by the intersecting lines. z = 1-t L1 x= - 1 +t y = 2 + 3t L2 x = 1- 4s y…

A: Given: L1  x=-1+t    y= 2+3t   z=1-tL2  x=1-4s   y=1+2s   z=2-2s To find equation of  plane by these…

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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 intersection point between the line      X=1+2t {    y=2-t       Z=3 and the x+y-z=3…

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Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0,1,1).

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Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0, 1, 1).

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Q: 2 4. Let Li be the line x = + s 1 and let L2 be the line x = +t|-1 a Find the point of intersection…

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Q: Find the point on the plane x + 2y + 3z = 13 closest to the point (1, 1, 1).

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Q: Find the point of intersection between the line x+2/6 = y - 3 = z/3 and the plane x + 2y – 4z = 0.

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Q: 2) The distance between the parallel planes ax + by + cz + d1 = 0 and |d1-d2| ax+by+cz + d2 = 0 is…

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Q: +3そ20 22 Prove that the line X21+2t ニー+3t is perpendicular to the plane X-2y+zz6

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: 5. Find the point of intersection of the given plane and line. Plane: 2x - y+3z=7 Line: x=-1+t y…

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Q: The curve intersects the plane (in a three dimensional space) y+z = 2 at the point ( (Hint: First,…

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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; -∞&lt;t&lt;∞L2: x=1-4s,y=1+2s,z=2-2s;…

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: 3. Among all the points on the graph of z = 10 – x² – y² above the plane x + 2y + 3z = 0, find the…

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Q: 4. How many solutions are there between the plane P₁: (x, y, z) = (4, −3,−1) + s(1, -3,1) + t(2,4,…

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Q: 17) An equation of a plane passing through the point ( 1, -2, 3) and containing the line L: x = 3 –…

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Q: find √x² ds along the line of intersection of the two planes X-Y+z = 0 and x+y+ 2z =0, From origin…

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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: 5/ Find the point at which the line through points P1(2. 3, 0) and P2 (-6. -3, 12) meets the plane…

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Q: Q1/: Find the distance between plane (6x - 2y - z +4 = 0) and point (3, 2, 1). (6 marks)

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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: find the line of intersection of th e given planes. 3x + 2y + z = -1 and 2x - y + 4z = 5

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Q: The line through the point (1, 0, 6) and perpendicular to the plane a + 3y + z = 5

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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…

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A: The two given planes are x-y+z=0 and x+y+2z=0.

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: find the line of intersection of th e given planes. 4x+ y + z = 0 and 2x - y + 3z = 2

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Q: Q:- find of the the line of interscetion plane given by 3X +6y -S2=-3 f the plane -2x + 79 -2=24

A: 3x+6y-5z+3=0 -2x+7y-z-24=0 Let z=t 3x +6y = 5t-3 -2x+7y = t+24

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

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Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

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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,…

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Q: Compute the intersections of the curve xy = 1 and the lines x +y = 5/2, x+y = 2, x+y = 0, x=0 , x=1…

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Q: intersection of the paraboloid z=x^2+5y^2 and the plane x=3. At what rate is z changing with y when…

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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: The pyramid is bounded below by the xy plane above by the plane x+y+z=3 and on the sides by the xz-…

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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 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: 5. Find the distance from the point (4, -3, 6) to the plane *-2y+z=1

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