Use Lagrange multipliers to find the distance from the point (3, 0, -1) to the plane 6x - 4y + 7z + 1 = 0.

Q: Find the distance between the planes 5x − 3y + z = 2 and 5x − 3y + z = −3

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Q: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x +…

A: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x + y…

Q: Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

A: Given : The equation of the planes are x+ 2y + 6z = 1 and x + 2y + 6z = 10 .

Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: B) Use Lagrange multipliers to find the points on the ellipse 2x2+y? = 1, where f (r, y) = ry has…

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Q: Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2…

A: Use Lagrange multipliers to find the points on the given surface that are closest to the origin.…

Q: Use LaGrange multipliers to find the points on the surface 2² = x² + y² which are closest to (4, 2,…

A: Given surface z2=x2+y2 and the point (4,2,0). The objective is to find the points on the surface…

Q: Find the distance between the planes 5x - 3y + z = 9 and 5x 3y + z = -2.

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Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

A: Let (x,y,z) be the point which is closest to the point (2,4,0) .

Q: Find the minimum distance from the point to the plane x- y +z = 6. (1, -6, 2)

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Q: Use Lagrange multipliers to find the minimum distance from the plane x+y+z=5  to the point (5,4,4) .…

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Q: Find the distance between the planes 5x - 3y + z = 9 and 5x - 3y + z = -6.

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Q: Find the distance between the planes x + 3y – 2z = 3 and 2x - y - z = 4. %3D

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Q: Find the distance from the point (2, 0, 0) to the plane x + 2y + 2z = 0.

A: Given a point, (2, 0, 0) and the equation of the plane x + 2y + 2z = 0.

Q: Use the method of Lagrange multipliers to find the shortest distance from the point (-2, –3, 1) to…

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Q: find the distance from the point to the plane. (1, 0, -1), -4x + y + z = 4

A: Concept -Let the equation of plane be -Ax+By+Cz+D = 0And the coordinates of a point be - (x1, y1,…

Q: Use the Lagrange multiplier method to find the point on the plane 4x +3y +2z = 0 with the smallest…

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Q: Use Lagrange multipliers to find the shortest distance, d, from the point  (1, 0, −2)  to the plane…

A: Lagrange Method:- The method of Lagrange multipliers is a strategy for finding the local maxima and…

Q: Find the distance between the planes. 5x-2y+z-4 0, 5x-2y+z+6= 0

A: Given,  Equation of Plane 1: 5x - 2y + z - 4 = 0 Equation of Plane 2: 5x - 2y +z + 6 = 0 From the…

Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: Find the distance between the point (0, 0, 0) and the plane 2x + 3y + z = 12.

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Q: Find the minimum distance from the point (6, 0, 9) to the plane x - y + z = 5. (Hint: To simplify…

A: Given plane is x-y+z=5 and the point is (6,0,9) normal to the plane is (1,-1,1)

Q: Use Lagrange multipliers to find the point on the plane  x − 2y + 3z = 6  that is closest to the…

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Q: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: 24) By using Lagrange multiplier find a point in the plane x+2y+3z=13 nearest to the point (1,1,1)

A: We have to find a point in the plane x+2y+3z=13 nearest to the point 1,1,1 by using Lagrange…

Q: 4. Use the method of Lagrange Multipliers to find the point on the plane r+y- 2 = 5 that is closest…

A: Given: The plane equation is x+y-z=5 and the point is -3, 5, 4.

Q: Find the distance between the given parallel planes. 2x - 3y + z = 8, 4x - 6y + 2z = 1

A: The solution are next step

Q: Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2…

A: Given data:   The given expression is y2=36+xz.   The expression of the distance of a point from the…

Q: Find the distance between the planes 4x + 6y – 2z = 4 and –2x – 3y + z = -3.

A: We have to find out the distance between two planes

Q: Find the distance from the point (1, 1, 1) to the plane 2x + 2y + z = 0.

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Q: Use the Lagrange multiplier method to find the point of the plane 4x-5y+3z=1 with less distance to…

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Q: Use LaGrange multipliers to find the minimum distance between the origin and the plane x+2y+3z=28.

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Q: Find √x²ds ds along the line of intersection of the two planes x-y+z=0 and x+y+2z=0, from origin to…

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

Q: Use Lagrange Multiplier to find the Point P (x,y,z) closest to the origin on the plane containing…

A: The equation of the plane passing through the three points can be obtained using the matrices. The…

Q: Use Lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point…

A: First note that ,          if (x,y,z) be any point on tha plane x-2y + 3z = 6 then distance between…

Q: Find the distance between the two parallel planes 5x – 3y + z – 2 = 0 %3D -10x + 6y – 2z + 3 = 0

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Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

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Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

A: Let the point on the cone is P(x,y,z). The the distance of the point P from the given point…

Q: Use Lagrange multipliers to find the points on the ellipse x2+2y2=1, where f(x,y)=xy has its extreme…

A: This question is related to Lagrange multipliers theorem. We will solve this question by using…

Q: Use Lagrange multipliers to find all points on the cone z2 = x² + y² that are closest to the point…

A: The solution has been given below.

Q: Find the point on the plane 3x + 2y + z = 6 that is nearest the origin.

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Q: Find the point on the circle x2 + y2 = 1 that is closest to the point (1, 3/4) by using the method…

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Q: find the distance from the point to the plane. (3, 0, 10), 2x + 3y + z = 2

A: the given point is (3,0,10) the given equation of the plane is 2x+3y+z=2 we have to find the…

Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

A: Given: Equation of cone is x2+y2-z2=0 and equation of plane is x+2z=4. To determine: The highest…

Q: Find the shortest distance between parallel planes 2x - 3y + z = 4 and 4x - 6y + 2z = 5

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Cone: z = √x2 + y2…

A: The surface of the cone               z=x2+y2 or z2-x2-y2=0                                (1)…

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

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to…

A: To Find: Use Lagrange multipliers to find the minimum distance from the curve or surfaceLine : x-y=4…

Q: Find the distance from the point to the plane. (3, 0, 10), 2.x + 3y + z = 2

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