The notation (x, y) → (-x, y) defines a reflection on the coordinate plane. O True O False

Q: In AABC, X is the centroid. If CW = 15 , find XW. %3D

A: Given,           In △ABC, X is the centroid and CW¯=15

Q: Find the trace of the plane in the given coordinate plane.3x − 9y + 4z = 5,  yz

A: The trace of the plane in yz plane is obtained by substituting x=0 in the given equation of the…

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

A: Find the condition for the given points to be collinear.

Q: C is the hexagon in the xy-plane with vertices (5, −5), (5, 5), (0, 10), (−5, 5), (−5, −5), and (0,…

A: Given : Vertices : (5,-5) , (5,5), (0,10), (-5,5), (-5,-5) and (0,-10) Integral given :…

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: find the trace of the plane in the given coordinate plane.  −x + y = 4, xz

A: Find trace of the plane in the coordinate plane -x+y=4 in xz

Q: – 3 (z – i)? +1 dz, i)² - (z – i)² | | where C is a closed contour traversed once in the…

A:

Q: Apply Stoke's theorem to calculate S. (x + y – 4)dx + (2x – z)dy + (y + z)dz, where C is the…

A:

Q: Assume that v lies in the yz-plane. Which of the following dot products is equal to zero for all…

A: The 3rd option is the correct option. Assume vector v in the y-z plane. The x-component for the…

Q: The notation (x, y) → (2x, 2y) defines a translation on the coordinate plane. O True O False

A:

Q: The notation (x, y) (1.5x, 1.5y) defines a rotation in the coordinate plane. O True O False

A:

Q: Evaluate ffz + 3y - x^2 ds where S is the portion of z=2-3y+x^2 that lies over the triangle in the…

A: To find the value of given fds over given region.

Q: w=f(z)=z/(1-z) under transformation IzI=3 Find the image of the circle?

A:

Q: i 1 4 fc 54 2 + z+5i (z+5i)® dz , Evaluate where C is the circle |z+ 5i| = 4 + 2, 0 < 0< 2 .

A:

Q: The notation (x, y) → (-x, y) defines a reflection on the coordinate plane, O True O False

A: Solving the problem by helping of a point.

Q: find the trace of the plane in the given coordinate plane.  −x + y = 4, yz

A: Let the plane P whose equation is;                                      -x+y=4…

Q: find the trace of the plane in the given coordinate plane.  3x + 4z = −2, xy

A: To find the trace of the plane in the given coordinate plane  3x+4z=-2 --- (1) in the xy plane

Q: f. Sketch the curve in the complex plane given by i. Iz - 3| = |z + 3i| ii. z? +z? = 2.

A:

Q: Use the flux form of Green's Theorem to evaluate |(6xy + 8y°) dA, where R is the triangle with…

A: Greens' Theorem : Let D be the region bounded by the curve C. Let F(x,y)=P,Q be the vector field…

Q: a) Evaluate f, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

A:

Q: (c) Let u(r, y) be the harmonic function in the disk B %3D

A: Given, u(x, y) be the harmonic function in the disk…

Q: 2 -2 0 -2 What are the coordinates of the image Ri90, o)(JKLO) = J'K'L'O? %3D J=(-3,1 K' = (-1,-5…

A: Find the points after rotation

Q: 2. Do the three planes x + 2y + z = 4, y - z = 1, x+ 3y= 0 have at least one commom point of…

A:

Q: (ii) Use the rescalings s = S/N, i = I/N, t = BN1, c = µ/(BN) and d = y/(BN) to non-dimensionalise…

A: differential equation representing disease with classes S , I , R dSdt=-βSI+γRdIdt=βSI-μIdRdt=μI-γR…

Q: Transform pentagon BEARS according to (xy) → (x + 6, y+8). Write the coordinates for pentagon…

A: Given Data: Traformation: x, y→x+6, y+8   The given figure in the problem represents the pentagon…

Q: If 0 is the acute angle between the planes x + y = 2 and x + y +2z =v 6, then 2cos (0) = 0 1 O 2 1/2…

A: Angle between planes is defined as angle between their normals.    Option  C is correct answer

Q: The notation (x, y) --> (x, y) defines a rotation on the coordinate plane. O True False

A:

Q: . Calculate the projection of å along b and projection of b along å when: d = 3î + j – k , 5 = -21 –…

A:

Q: Let h, r be constants. Consider the quadric surface S of equation (x – h)? (y – 1)² (z – r)2 9 3 The…

A:

Q: Find /| F-dS if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = = 8-x?-y? lying…

A:

Q: The coordinates of ADEF are D(-1,4) , E(7,-3), and F(9,5). Write a rule for the translation of ADEF…

A: To write- rule for translation.

Q: Let 3 6. 6. 4 11 j = 14 For what value of h is y in the plane spanned by vị and v2? h =

A:

Q: Transform pentagon BEARS according to (x, y) → (x +6,y+B). Write the coordinates for pentagon…

A:

Q: 2. Do the three planes X + 2y + z = 4, y - z = 1, x+ 3y = 0 have at least one commom point of…

A: The equation of the plane is given by the formula ax+by+cz+d=0. The system of planes can be solved…

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: Find a parametric representation of the solution set of the linear equation x+y+z=1 x=1-2t, y=t, z =…

A: Solution

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

A:

Q: Let a = 4i + 3j – k, b = 2i – j + xk and c = yi + zj – 2k. Find: %3D %3D a x such that a and b are…

A: Two vectors are said to be perpendicular to each other if their dot product is zero. We will use…

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

A: Surface integral

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

A:

Q: where F(x, y, z) = (ry, x²y, y) Use Gauss's theorem to calculate where is the paraboloid z = 4 – x²…

A:

Q: Which of the following represents a plane surfac whose x-, y-, and z-intercepts are a, b, and c…

A:

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

A:

Q: Determine the angle between the following two planes: −x + 6y + 3z − 6 = 0 2x + 3z − 10 = 0

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Q: The notation (x, y) (-x, y) defines a reflection on the coordinate plane. O True O False

A:

Q: Given F(x.y.z) (x+y+Zi +(x-yj+(xz-2)k what is CurlF at the point (1,-1,3)? You should write your…

A:

Q: 17. Find the angle between two planes below. a. 2x- y+= =5 and 3x + y-z =1 b. 2x - 4y + 6z = 1 and…

A: