Po (2,1,-1) and perpendicular to the line of Find a plane that passes through intersection of the planes (2x + y – z = 3) and (x + 2y + z = 2)?

Q: We have two planes in IR, defined by equations I- 3y+z -7 and 2 +y+2z = 0. These two planes…

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Q: Find an equation of the plane through (-1, 2, -5) and perpendicular to the planes 2x- y+z = 1 and…

A: We are  authorized to answer one question at a time, since you have not mentioned which question you…

Q: 4. What is the equation of the plane through (-1,-1,0) parallel to the plane x + 2y+ 3z 9? (a) x -…

A: To find the equation of a plane through (-1,-1,0) parallel to the plane x+2y+3z=9

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

A: We find required equations of plane parallel to given plane.

Q: Consider that planes of equations 2x +y - 3z =1 and x+3y +z = -2 a) Show that the planes intersect.…

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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: b. Find the distance from the point (2, –2, 3) to the intersection of the planes 2x – y + 3z = 1 and…

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Q: Consider the planes of equations −y+z−2=0 and x−y=0. a) Show that the planes intersect. b) Find…

A: We can solve this using definition of intersection of plane

Q: Among all the points on the graph of z = 11-x² - y? that lie above the plane x+ 5y + 6z = 0, find…

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Q: Determine the general cquation of the plane 2 passing through the point P(1,-4,-5) and parallel to…

A: We have to find equation of ohm plane

Q: Find an equation of the plane. The plane that passes through the line of intersection of the planes…

A: x - z = 2 ⇒ x = 2 + zy + 3z = 2 ⇒ y = 2 - 3zLet z = t then parametric equation for the line of…

Q: plane

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Q: 11) The distance from the point S(7, 6, -8) to the line x = −2 + 4t, y = -9 + 3t, z = 3 + 12t 12)…

A: #11) Given: Point = S7, 6, -8 and the line x=-2+4t, y=-9+3t, z=3+12t. To find: We have to find the…

Q: Consider that planes of equations 2x + y - 3z = 1 and x+ 3y +z = -2 a) Show that the planes…

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Q: The endpoint of a line segment  is at  P1(–2, 1, 6)  and the  midpoint Q  lies on the plane  y = 3.…

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

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Q: Determine the general equation of the plane 2 passing through the point P(1, -4, –5) and parallel to…

A: Given problem:- Determine the general equation of the plane π passing through the point P(1, -4,-5)…

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

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Q: Find a plane containing the point (1, 3, 3) and the line of intersection of the planes - 2x - 3y -…

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Q: 39. The plane that passes through the point (1, 5, 1) and is perpendicular to the planes 2x +y - 2z…

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Q: Find the line of intersection of the planes 2x+y-z=3 and x+2y+z=2. Find the equation of the plane…

A: Solution of part (a) in step2 and step3 and part (b) in step4.

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: The plane containing the point (-7,-1,0) and parallel to the plane 5x + 8y – 2z Ax+By+ Cz = D. If A…

A: Given the plane containing the point (-7,-1,0) and parallel to the plane 5x+8y-2z=-5 has the…

Q: Find an equation of the plane. The plane through the point (6, −8, −8) and parallel to the plane…

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Q: Consider the plane x-y-z-8= 0. Find the point in this plane closest to the point (1, 0, 1).

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Q: 10. The distance between the point (3,-2,5) and the plane 2x+2y+z=5 is NONE

A: Given: The distance between (3,-2,5) and the plane 2x+2y+z=5

Q: The planes 3x + 6z = 1 and 2x + 2y - z = 3 intersect in a line. a. Show that the planes are…

A: Given,

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

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Q: 1. Find the distance between the two planes - 2y + z=4 and z-2y+ :-1 HI

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Q: the

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Q: Find an equation of the plane. The plane through the point  (3, −4, −7)  and parallel to the plane…

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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: Find the intersection of the two planes with equations 3(x – 1) + 2y + (z + 1) = 0 and (x – 1) + 8y…

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Q: 7 Find the Paametric equ. for the line f intersect of the Planes 3x- 6y -2z =15 and 2X+Y-22%3D5?…

A: Given two lines, 3x-6y-2z=15 ....(i) and 2x+y-2z=5....(ii) Putting z=0 in (i) and (ii) we get,…

Q: Find the equation of the plane contains the line X+1/2 = Y/3 = Z-1/4 and the line of intersection of…

A: We have given the line of intersection of planes; x + 2y - 2z = 6 , 5x - 2y - z = 0 and line; X+1/2…

Q: Find an equation of the plane. The plane through the point  (8, −3, −3)  and parallel to the plane…

A: We know that two parallel planes have same direction ratios(i.e. the coefficients of x,y and z…

Q: The planes 3x + 6z line. = 1 and 2x + 2y - z = 3 intersect in a a) Show that the planes are…

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

A: Given :-  The plane determined by the intersecting lines. L1    :   x = -1 + 3t    ,    y = 2 + 3t…

Q: 12. Find the distance between the point (3,-2,7) and the plane 4x – 6 y + z = 5.

A: The equation of plane is 4x-6y+z=5 and the given point is 3,-2,7. The distance between the point and…

Q: (1 point) Find the point at which the line (-2, 1, –5) + t(-1,–1, –2) intersects the plane 4x – 2y +…

A: To findcthe point at which the line (-2,1,-5)+t(-1,-1,2) intersects the plane 4x-2y+2z=-68

Q: Find an equation of the plane. The plane that passes through the line of intersection of the planes…

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

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

Q: Q = (-1,3,–1) on the plane Find the point P nearest to x – 4z = 2

A: Given, Q=(-1,3,-1) x-4z=2 (equation of plane) x-4z-2=0

Q: Find an equation of the plane. The plane that passes through the line of intersection of the planes…

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Q: . Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x - y + z =…

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Q: 5. Cakculate the distance between the point (3. 1. -2) and the plane 2x + y - z+1-0 O 10 /14 O -10…

A: Find the distance between point and plane?  Value of k for det A= -4

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: Consider that planes of equations 2x +y - 3z =1 and x+3y +z = -2 a) Show that the planes intersect.…

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