3 Show that the planes, x-2y+4z-13D0 and 3x-6y+8z=5, if so, find the distance * .between them 2/3(12)^0.5 3/(21)^0.5 1/3(12)^0.5 Non of all

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

A:

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

A: Given equation of planes: 2x-3y+z=4 and 4x-6y+2z=5. To find: Shortest distance between the parallel…

Q: prove that the three planes 2x+y+z = 3 , x-y+2z = 4, x+z = 2 from a triangular prism and find the…

A:

Q: Find the distance between the parallel planes P and P2 P: 2x-y+ 3z 6 = 0 P2: 6x - 3y+9z+ 6 = 0 8 *…

A:

Q: 9. Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

A:

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: 5z' + 3z gral z² - 4 plane, is

A:

Q: 4. Find a plane through Po(2, 1, –1) and perpendicular to the line of in- tersection of the planes…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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

A:

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

A:

Q: 4 Find a parametrization for the line segment with endpoints (-1,3) and (3,-2).

A: 4) To find the parametric equation of line segment with endpoints (-1,3) & (3,-2)

Q: Find the distance between these two planes x + 2y –' 2z = 3 and 2x + 4y - 4z = 7.

A: Devide the equation of 2nd plane by 2 .we get that both planes are parallel so just apply formula…

Q: 5. Among all the points on the graph of z = 10 – x² – y² that lie above the plane r+2y +3z = 0, find…

A:

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

A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…

Q: Find the distance between the planes 3x-y+6z=7 and -6x+2y-12z=1. Round off answer to four decimal…

A: Given: To explain the correct option of the given statement as follows, The given planes are 3x-y+6z…

Q: 14) Determine the distance between the parallel planes: 6z = 4y – 2x; and 9z = 1 – 3x + 6y.

A: Given:-planesP1: 6z=4y-2x2x-4y+6z=0x-2y+3z=0P2: 9z=1-3x+6y3x-6y+9z=1x-2y+3z=13To find : distance…

Q: Find the shortest distance from the point P(2,-1, 1) to the plane with =quation x - y + 2z = –1 and…

A: Shortest point of the given plane and point P.  Distance from the point P and Q

Q: Find all planes in R^3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

A: To find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.…

Q: Find the distance between the parallel planes 4x – 3y + 12z = 12 and 4x — Зу + 12z 36.

A: In this problem we have to find distance between two parallel planes.

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

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

A:

Q: 5. Evaluate 2XZds where S is the part of the plane - 2x +4+Z =3 over the triangle with bounds…

A:

Q: Find the point P nearest to Q = (−1, 3, −1) on the planex − 4z = 2

A:

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

A: Given:

Q: The distance from the point K(3, -2, 0) to the xy-plane is Select one: 3 -2

A: Find out the correct option.

Q: 5) Find the distances by drawing the figures and right triangle used to calculate a. Between 1₁ =…

A: Given: Let's determine the distance for the following, a) medium of l1=2+2t,-1+t,-3t and…

Q: 3. Use LaGrange multipliers to find the point on the plane 2r - y+4z = 10 that is closest to the…

A: Use Lagrange method to find point

Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: Among all the points on the graph of z = 10-x2 -y² that lie above the plane r+2y+3z = 0, ind the…

A: Given that z=10-x2-y2 and x+2y+3z=0 Find the point which is farthest from the plane.

Q: 5. Parallelogram RSTU with vertices R(-2, 3), S(2, 4), T(2,-3), U(-2,-4) over the line y = x ty 6.…

A:

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 shortest distance between (3,4,1 ) and the plane X+y +Z = -2

A: Using distance between plane and point formula we can calculate.

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: Find the distances (a) Between l1 = (2+ 2t, –1+t, -3t) and l2 = (4, -5 – 3t, 1+ 4t) (b) Between the…

A:

Q: Find the distance from the point (0,8,9) to the plane – 2y + 3z = 11.

A: In this question, we will find the distance from the given point to the given plane.

Q: 14) Determine the distance between the parallel planes: 6z = 4y - 2x; and 9z = 1- 3x + 6y.

A: Given problem:- Determine the distance between the parallel planes: 6z = 4y - 2x and 9z = 1 - 3x +…

Q: Usually there will be exactly one hyperplane in Rn that contains the n given points x = 0, a1, ... ,…

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Q: Find the area of on of the triangle that can drawn between the planes Зх — бу- 2г 15 and 2x + y - 2z…

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Q: Determine the set of points satisfying the condition described by |z – 3| + |z + 3| = 10 Then…

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Q: Find the families of characteristics of the PDE (1-x²)w„ - u,, = 0 in the elliptic and hyperbolic…

A: Pde

Q: Find the distance between the point (1,3,-1) and the plane 3x - 4y + 5z = 6. (Enter an exact answer…

A: Given point 1,3,-1 and the plane 3x-4y+5z=6

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

A:

Q: Find the shortest distance from the point (1, 0, −9) to the plane x + 2y + z = 9.

A: Given plane isx + 2y + z = 9and point (1, 0, -9)We have to find shortest distance

Q: The distance between the centers of the following two spheres: x2+56x+y2−54y+z2=−1512,…

A: A detailed solution is given below

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

A: Two planes  and will always be parallel if The given planes  and  are parallel because we can see…

Q: Find a plane containing the point (-4,4,2) and the line of intersection of the planes -3x + 8y + 2z…

A: