Calculate gij for the distance between (x;) = (1, 1, – 1) and (yi) = (0,1,2) in %3D T-2 1] barred coordinate system i = Ax , where A = 3 1 2 -2 3]

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

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Q: 1. Consider the family of curves 1 y = Vx +C Find its domain. Find the specific member of orthogonal…

A: first we will find the domain of the given function then we will find the differential equation…

Q: Find a parametrization of the vertical line passing through the point (9, 5, 0) using t = z as a…

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Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

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

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Q: Find the equation of the tangent plane to th surface 3x? + 5y? + 4z2 = 24 at the point (1, –1,2). 1.…

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Q: Chapter 11, Section 11.4, Question 029a Consider the parallelepiped with adjacent edges u = 5i +…

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: Find the ar ea of sur face x - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2,…

A: Given :          The surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x…

Q: Find a parametrization of the line through P = (4, 9, 8) perpendicular to the yz-plane.

A: Equation of Linethe Line through P =(x0,y0,z0) in the diresction of vector v→=(a,b,c)is defined…

Q: Find the point(s) on the plane 4x +3y +z = 2 that are closest to (1,-1,1).

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Q: Determine the location of a point (x, y, z) that satisfies the condition  ∣y∣ ≤ 3

A: If ∣y∣ ≤ 3 the point lies with in 3 units from xz plane on left side if y < 3 , or within 3 units…

Q: Compute Sc(2x + V) ds, where C is the curve from (0,0) to (2, 4) along y

A: Given

Q: Determine the Eq.  of plane (M) pass through points A(0,2,0), B(1,1,1), C(-1,0,2)

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Q: F - dr where F(x, y, z) = (4.25yz cos(xyz), 4.25xz cos(xyz), 4.25zy cos(ryz)) Evaluate п 1 and Cis…

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Q: Integrate ƒ(x, y, z) = x - 3y2 + z over the line segment C joining the origin to the point (1, 1, 1)

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Q: Find the distance from the point (-4, 5, 1) to the plane – kr – ly – 2 = 5.

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Q: What angle does the line of interaction of the planes 2x+y-z = 0 and x+y+2z= 0 make with the…

A: The direction vector of the line of the interaction of the two planes is equal to the cross product…

Q: Find the condition for the points (a,0),(h,k),(0,b) when ais not equals to 0 to be collinear

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Q: 8. Determine the equation of the plane tangent to z point (x, у, z) 3 (-2, 1, 4). x*y3 at the =

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Q: A _____ is the set of points (x, y) in a plane such that the difference in distances between (x, y)…

A: The standard form of the equation of the hyperbola is,

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 1 + 6t, z = 2t,…

A: Explanation: Given that,  Line 1: x=1+ty=1+6tz=2t Vector 1: 1,6,2 Line 2: x=1+2sy=5+15sz=-2+6s…

Q: Consider the inmplicitly defined curve xy +3x2 4. %3D O Verify that the point (1, 1) is on the…

A: Consider, the implicitely defined curve                          xy2+3x2=4 We have to verify the…

Q: The value of the line integral I- [Adl where A-(2x+y)£+(y-x)ý along the parabola y=x^2 and form…

A: Evaluate: I=∫A.dl              ...(1)WhereA=2x+yx∧+y-xy∧

Q: A(n)________ is the collection of points in the plane the difference of whose distances from two…

A: The given statement is "A(n)________ is the collection of points in the plane the difference of…

Q: 1. A such that the difference in distances between (x, y) and two fixed points (called is the set of…

A: A___ is the set of points (x, y) in a plane such that the difference in distances between (x, y) and…

Q: Find the distance between the given point and the given plane. Point: (−1, 4, −2) Plane: x+2y+z=3

A: We can use distance formula to calculate the distance.

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

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Q: 7. Find the distance between the point (3, 1, –2) and the plane x + 2y – 2z = 4.

A: Given that plane x+2y-2z=4 and point 3,1,-2To find :Distance between point and plane Solution if…

Q: A line segment bounded by two points (0,0,0) and (2,2,0) is rotated about the y-axis by 270 degrees.…

A: We will first parametrize the line as a function of t , then with the help of rotation (u) matrix we…

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

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Q: Let C be the line segment from point (0, 1, 1) to point (2, 2, 3). Evaluate line integral yds. C

A: To evaluate the line integral

Q: Find the distance between the skew lines with parametric equations  x = 1 + t, y = 3 + 6t, z = 2t,…

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Q: Find the condition for the points (a, 0), (h, k), (0, b)when ais not equals to U to be collinear

A: We have to find the condition

Q: Compute ,f for f(2) +6 + 6i, positively oriented. sin(32) and path 2 that is the boundary of the…

A: Let's see the method of integration. We use residue method to solve this integral.

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: 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: Evaluate aned on c indicatid curve 2. 2. y+ Y( sm3x +ca 32,22 3t ,4=t,0zt2|

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

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Q: Find the distance between the point (3,11,-2) and the plane X t 2y

A: Explanation of the answer is as follows

Q: find the equation of the line through (0,2,1) that is perpendicular to both u= 4i + 3j − 5k and the…

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Q: Find a parametrization for the ray (half line) with initial point (-4,3) that passes through the…

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Q: Find the coordinates of the point Y that lies 2. along the directed line segment from X(-1,3) to…

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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: Use Green's Theorem to evaluate $. xydx + x²y³dy, where C is the triangle with vertices (0,0), (1,0)…

A: Consider the provided question, ∮cxydx+x2y3dy,     where c is the triangle with vertices 0,0, 1,0…

Q: Find the distance between two skew lines x = 5+t, y = 5 + 3t, z = 4 -t and x = 2t, y =t, z=t O 1 3 '…

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Q: Find the equations of the tanget plane and normal line to the graph of In(z2) x -= 3y³ – Vx at the…

A: Given graph is                                                        lnz2x-eyx=3y3-x Again…

Q: Obtain the dirfferential equation of the family of plain curves given 1. All circles passing…

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Q: Find the point on the plane x+y+z%3D24 that is closest to the point (1,1,1).

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

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.