If (V3, -3, -V4) is the rectangular coordinate of the point p, then the spherical coordinate of p = (p,0, 6) is: A) (4, ) 3 B) (4, 등, 풍) 11т 5л 6 C) (4,) 57 T , 3: 3 D) (4. 5.) E) (4, 똥, 좋) 57 27

Q: The angle between two planes is the smallest angle 0 between the planes 6x + 2y – 4z = 0 and - 7x +…

A: We will solve the problem

Q: Explain how spherical coordinates are used to describe a point in ℝ3.

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

A: Given:   3x + 2y + 6z = 5     Point: ( 1 , -4 , 6 )

Q: Convert the following point from spherical to rectangular coordinates: 5, 3'3 - (x, Y, z) = Usage:…

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Q: Name three points Coplanar with point A

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Q: What are the cylindrical coordinates of the point whose rectangular coordinates are (x = 4, y = 5, z…

A: A rectangular coordinate or cartesian coordinate system is a system that specifies the position of a…

Q: If the spherical coordinates (p, 0, ) of a point P are (1, 0,), then the Cartesian (rectangular)…

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Q: For what positive value of c is the acute angle between the plane containing the points A(0,0,1),…

A: The equation of the plane passing through the three non-colinear points x1,y1,z1, x2,y2,z2, and…

Q: Express the point given in Cartesian coordinates in cylindrical coordinates (r, 0, z). A (예), 에(¥),…

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Q: What are the rectangular coordinates of the point whose spherical coordinates are (1, ½π, π) ? x = Y…

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Q: Convert from cylindrical to rectangular coordinates ( a) ( 4, π/6, 3 (b) (8, Зт/4, -2) (c) (5, 0, 4)…

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Q: Find the distance of point A(1,0,2) to the plane 3x+y+z=9?

A: Here we have to find the distance from the point A(1,0,2) to the plane 3x+y+z-9=0

Q: Convert the points (x, y) = (1, −3), (3, −1) from rectangular topolar coordinates.

A: When point in cartesian coordinates x,y and convert into polar coordinates r,θ then first find the…

Q: Convert the point (x, y, z) = (– 4, 2, 5) to spherical coordinates. Give answers as positive values,…

A: We are asked to convert  to spherical coordinates.

Q: Convert the point (æ, Y, z) = (0, 2, 3) to spherical coordinates. Give answers as positive values,…

A: x,y,z=0,2,3We have to calculate the spherical coordinates.As we know that cartesian to spherical…

Q: show that the points AC!,l,4) B(2,2,2), coplanear (in the c(o,l,5) and D (1,0,5) are Same plane).

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Q: If we convert the point (p, 0, 6) = (6,7/6, 5T/6) from spherical to cartesian coordinates, we obtain

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Q: Convert the point from rectangular coordinates to spherical (3, 0, 0) (p, 8, 4) = ( %3D

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Q: If point P has cylindrical coordinates 6, 8 then its rectangular coordinates are 3 (x, Y, 2) =

A: Finding the rectangular (or) Cartesian coordinates

Q: Convert the point (x, y, z) = (2,2v3, 4) to spherical %3D coordinates (p, 0, 4).

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Q: Find the rectangular coordinates of the point P with cylindrical coordinates (r, θ, z) = (5, 5π/4,…

A: Given, cylindrical coordinates (r, θ, z) = (5, 5π/4, 6)

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

A: Given : Point : 1,-2, 4 Plane : 3x+2y+6z = 5

Q: The midpoint of AB is M(0, –4). If the coordinates of A are (2, –1), what are the coordinates of B?…

A: Given- The midpoint of ABis M0,-4. To Find- The coordinate of point B, if the coodinate of the point…

Q: The Product of the triple integrtion use Sphericalcoordinates 2. 11 B/

A: Here is the solution of the given problem.

Q: Explain how cylindrical coordinates are used to describe a point in ℝ3.

A: The Cartesian coordinate system provides a straightforward way to describe the location of points in…

Q: The location of a point on the Cartesian coordinate system (x,y,z) is (4,5,6). Using the location in…

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Q: Find the point on the plane 2x + y + 4z = 5 that is closest to the point P(4, 3, 5). (x, y, z) =…

A: We are given a plane 2x + y +4z = 5, and we are asked to find the co-ordinates of the point on the…

Q: Find the equation of the plane that contains point P(1, -1, 2) and has the normol n= 2¿+3j+Sk.

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Q: the Cartesian coordinates of the point with cylindrical coordinates (r, 0, 2) = (4, т, 6) (x, y, 2)…

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Q: Determine the location of a point (x, y, z) that satisfies the condition z = −5

A: The condition is z = −5

Q: What are the rectangular coordinates of the point whose spherical coordinates are (2, 응까, -3짜) ? x =…

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

A: Distance from point to plane formula If Ax + By + Cz + D = 0 is a plane equation, then distance from…

Q: 4-) Find the a Cute augle between the liue joning the two Points ACY2,3),B(5,1,7) , and the Plane…

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Q: Find the distance from the point (-2, 1, 4) to the plane z = -1

A: Given, plane z=-1 and the point (-2,1,4)we have to find the distance from the given point to the…

Q: (d) Convert the following point from rectangular to spherical coordinates: -3/6 -3/6 -3 2 (р, 6, Ф)…

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Q: 2. Convert the point (V6, , v2) from cylindrical to spherical coordinates. (e) (2VZ,품, 끌) (d) (vZ )…

A: The solution is given as

Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is

A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.

Q: 1. Find the distance from the center of the sphere given by (x-2)² +(y+2)²+(z-1)² = 4 to the point…

A: Given equation of the sphereis x-22+y+22+z-12=4So center of the sphere be 2,-2,1and the given…

Q: Find the point cylindrical coodinater of whoose cartesin coordinates are 10,-1,2)

A: Given: The cartesian coordinate (0,-1,2)

Q: What are the rectangular coordinates of the point whose spherical coordinates are (1,,)? x = 0 y = z…

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Q: Find the rectangular coordinates of the point whose spherical coordinates are given. (a) (1, 0, 0) -…

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Q: Find the rectangular coordinates of the point, whose cylindrical coordinates are given. (a) (4, T/4,…

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Q: Is it possible to draw a square in spherical geometry?  Please explain your answer.  How does your…

A: Square in spherical geometry is possible?

Q: One set of cylindrical coordinates of the point with the rectangular coordinates (2, 2, 4) is:…

A:

Q: (2, 1) is the midpoint of AB, in which A has coordinates (8, 10). Find the coordinates of B.

A: given: (2,1) is the mid point of AB. the coordinates of A are (8,10) we have to find the coordinates…

Q: Find angle between two planes given by 2x + y – z = 29 and 3x + y + 2z = 6. %3|

A: we have to find the angle between the two planes given by 2x+y-z=29 and 3x+y+2z=6. the equations of…

Q: Consider the spherical coordinate point (3,7, (3,1) Convert to Cartesian coordinates.

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Q: Find the distance of the plane passing through the points ā, b, c from the origin.

A: First we derive the vector equation of plane.    The perpendicular distance is the projection on the…

Q: For what positive value of c is the acute angle between the plane containing the points A(0,0,1),…

A: Calculate the vector normal to the yz plane. Equation of yz plane:x=0Equation of vector normal to yz…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.