Given, | (2z – z) dz along the directed line segment from – i to 1. What is a parametric form of z(t)? t+ i(1-i) 21 – i(t– 1) 2t + i(t- 1) t+ i(t- 1)

Q: 4. Consider the point M 2t,31 – 1,-t+ Determine t for that M belongs to the mediator plane of [AD].

A: Question: (4) Given points A-1,4,2,B1,1,0,C-3,5,-32 and D232,15,10 Objective is to find the value of…

Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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Q: Consider the following. 3x + 3y + 6z = 54 Sketch a graph of the plane. NO 10 10 10 10 10 20 20 20 20…

A: To find x intercept substitute y=0 and z=0 To find y intercept substitute x=0 and z=0 To find z…

Q: Find the point on the plane x+5y+2z=14 closest to the point​ (1,1,1).

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Q: Calculate , z² dS if S is the prism whose base is the triangle in the limited xy plane by the x axis…

A: Here given figure is Since prism has 5 surfaces (1)-OAB (2) OADE (3) CDE (4) OBCD (5) ABCE

Q: Find the projection of d on the plane P if a 4 and P has the equation x + y+ z = 1.

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Q: Let C be the line segment joining A(1,1,-2) to 0(0,0.0). A parameterization of C is given by* None…

A: NOTE : As per Bartleby guidelines only one question will be answered. Please upload other parts…

Q: Draw a picture on the z-plane

A: In this question, we draw a picture of the given curve in C(t). here, first, we write the real and…

Q: 6. Given a rule x² + y² = 9, its image rule x? + y² – 2x + 6y +1 = 0 under a translation, state a…

A: To solve the given translation problem.

Q: 4. Consider the curve in the plane defined by r3+y3 = 6xy. %3D (a) Find for any point (r, y) on the…

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Q: Given, (2z – z) dz along the directed line segment from -i to 1. What is a parametric form of z(t)?…

A: We have to find the parametric form of directed line segment from -i  to 1

Q: 5 3 - 2 Let y = 1 Find the distance from y to the plane in R° spanned by u, and uz. -2

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Q: Parametrize the directed line segment which joins the point −2 + 3i to the point 5 − 7i, that is,…

A: The parametric equation on a line passing through the points x1,y1 and x2,y2 is given as follows:…

Q: 9. Let the affine map A : R? → R² be defined by A(x, y) = (3.x + 4, 2y – 3). Show that %3D the image…

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Q: use green's theorem to evaluate ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4 counterclockwise

A: Given: ∫c 5y^3dx-5x^3dy where C is the circle x^2+y^2=4

Q: 6. Given a rule x2 + y2 = 9, its image rule x2 + y2 – 2x + 6y + 1 = 0 under a translation, state a…

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Q: Given, (2z – z) dz along the directed line segment from - i to 1. What is a parametric form of z(t)?…

A: We have to form a line segment from -i to 1 Let 0≤t≤1

Q: Let T be the plane x – y – z = 7. Which of the following planes are orthogonal to T and pass through…

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Q: 4. Evaluate . F.ds , where C is the triangle with vertices (1,0,0), (0,2,0), and (0,0,3) oriented by…

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Q: show. that theAine in.which.the planes.X+.2y-22=-5 nod5X-2y.z=.0...jntersec.is..pavalle.to.theine.…

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Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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Q: Sketch the plane curve. r(t) = 3ti - tj, [0, 3] O y 3 2 1 -1 -26 " 3₂ 3 2 1 -1 -2 2 4 4 Find its…

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Q: 3. Use Green's Theorem to evaluate G³ï+xj)•dr around the perimeter of the rectangle 0<x<2,0<y<3.…

A: Given ∫C(y2i+xj).dr We know that dr = dxi+dyj Thus ∫C(y2i+xj).dr = ∫C(y2i+xj).(dxi+dyj)  =…

Q: 7. If 1x, y2 are the coordinates of a point P in the xy-plane,then x is called the__________________…

A: Given that, x,y are the coordinates of a point P in the xy-plane. The objective is to fill in the…

Q: Let F = (tan(3x) - y)i + (2x – sec-1y)j and C be the boundaries of the circle x2 + (y-4)2 = 9 in the…

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

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Q: C is counterclockwise around the rectangle with vertices (0, 0), (5, 0), (5, 3), (0, 3) (a) directly…

A: The given integral is: ∮xy dx+x2 dy C is the counterclockwise around the rectangle with vertices…

Q: Зу — 2z 3D 6

A: Use a graphing utility to plot the plane, 3y-2z=6 .

Q: Let F(x, y, z)=z²i+ 2xj+y°k and let S be the graph of z = 4-x² -y², z 20 oriented counterclockwise.…

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Q: Consider the following. 3x + 3y + 7z = 63 Sketch a graph of the plane. 10 Z10 10 10 10 10 20 20 20…

A: The equation of the plane is given as , 3x+3y+7z=63 sketch the graph of the plane.

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: 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: 2. Let C be the closed path constructed by joining the segment [-2, 2] on the real axis with y(t) =…

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Q: Find the condition for the points(a, 0).(h, k)(0, b) when ab 0 to be collinear.

A: When points are colllinear area should be 0Therefore, 12a01hk10b1=012ak1b1+1hkb1=0

Q: 9. Suppose that a : R³ → R³ by perpendicular projection onto the plane 3x – 2y + z = 0. Find ↑

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Q: (b) Find the points on the line r(t) = (t, 1+2t, 1-2t) whose distance from the plane 2x - 2y+z=1 is…

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Q: Find i x w if ||T|| = 3, ||w|| = 4, 0 = and ī, w both lie in the xz-plane (as shown). 3 %3D

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Q: Let Ci be the rectangle with vertices (0,0), (2,0), (0,1), and (2,1) oriented counterclockwise, and…

A: Let C₁ be the rectangle with vertices (0,0). (2,0), (0, 1), and (2,1) oriented counterclockwise, and…

Q: Consider the following. 3x + 3y + 6z = 54 Sketch a graph of the plane. Z10 10 10 10 10 10 20 20 20

A: intercept form is  xa+yb+zc=1 where (a,0,0) (0,b,0) and (0,0,c) are intercept at x,y,and z axis

Q: 4. let f(x, y) = x² – xy + y² – y. find the direction u and Duf at Po(1,–1) for which Duf is the…

A: Given:- f(x, y) = x2 -xy+y2 -y To find:- Direction u and Du f at point p0 (1, -1) for which Du f is…

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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Q: Evaluate I = Se(sin æ + 7y) dæ + (3x + y) dy for the nonclosed path ABCD in the figure. А 3 (0,0),…

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Q: Given, (2z - z) dz along the directed line segment from -i to 1. What is a parametric form of z(t)?…

A: Given integral ∫Γ2z-z¯dz where Γ is the line segment from -i to 1. i.e., it is a line segment from…

Q: Find b such that B = (0, b) has hyperbolic distance of u from the point A (0,0).

A: Given: B=(0,b) has  hyperbolic distance of u from the point A=(0,0) Formula used:

Q: c. Let P(x, y) = y² + sin¬1 x² and Q(x, y) = 2xy + 4x. Suppose that C is the parallelogram with…

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Q: The curl of f(x,y,z)=xyzj is None of these. хуk-yzi О ху-yzk ООО О

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Q: Let C be the boundary curve counterclockwise of the semidisk æ? + y? 0. Then fc(-2ydx + 3xdy) 5dydx…

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Q: Let P be the plane 2r + u – 7 = 2 and let 0(1.0.3) be a poir

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Q: Given Fxy 2) = (z², xy, yz) and C is a triangle in the plane x + y + z = 2 with vertices (1,1,0),…

A: We will use basic knowledge of vector calculus.

Q: 2 Let w = z². Find the image of the first quadrant in z-plane

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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.