1-8. Prove that, for any differentiable vector u Eu(t), dv du

Q: Prove that if u is the vector function with the constant value C, then du/dt = 0.

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Q: Suppose a vector function F(x, y) = 3xi + 2xyj + y ln z k moves along a path C where x = t², y = t +…

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Q: - draw the vector fields . F(xy) = 2xi – yİk

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Q: Given vector field A = 5p sinø a, - pz cosø a, + 2p a̟. At point P(1, T, -1), the vector component…

A: A= 5ρsinϕaρ-ρzcosϕaϕ+2ρaz  at point  P(1,π,-1) =0aρ-1aϕ+2az A that is parallel to  ϕ =π is…

Q: (1) Is the vector field F(x, y) = (2æ*y^ + æ) î + (2a*y³ + y) Î conservative? Support your answer…

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: In order for vectors and t- 3 in a vector space R3 to be linearly t+4 in depen den t what should t…

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Q: 2.10 (a) Express the vector field H = xy'za, + x'yza, + xyz'a. in cylindrical and spherical…

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Q: Express the vector field B = (x^2- y^2)ay + xzaz in spherical coordinates at ( 4, 30o, 120o) *…

A: Relation between cartesian and spherical co ordinate system x= r sinθ cosϕ   , y = r sinθ sinϕ   ,…

Q: Match the vector field with its graph. F(x, y) = xi + 3yj + +x ' ||||||||||| 畫 至 X

A: Solution is given below:

Q: Compute and sketch the vector assigned to the points P = (1, 2)and Q = (−1, −1) by the vector field…

A: Given the vector field and the points

Q: If A is second order tensor , then |A| =T^i

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Q: Compute and sketch the vector assigned to the points P = (0, 1, 1) and Q = (2, 1, 0) by the vector…

A: Solution:Given       P = (0, 1, 1) and Q = (2, 1, 0)F=<xy,z2,x>To sketch the graph of F

Q: 41.) Use given grid to sketch the vector field F = (y, -x). Include vectors at all integers points…

A: Given vector field is F=12y,-x

Q: 15) Consider the vector field F (x, y, 2) = (In y, x, z) and the oriented curve C:r (t) = (t, e', 2…

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Q: a. The zero vector 0 is in ker(A) b. If x and y are in ker(A), then so is z = x + y. c. If x is in…

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Q: Let F (4t +3, sin(3t), 42) Find the indefinite vector integral | F(t) dt = ( +C1, +C2, +C3)

A: Given,F=4t+3,  sin(3t),  4t2∫F(t)dt=?

Q: Two vector fields are F = -10 ax + 20 x (y–1) ay and G = x y ax – 4 ay + z az. For the point P(2,…

A: Given vector fields are F=-10 ax +20 xy-1 ayG=2xy ax -4ay +z azPoint P =2, -3, -4

Q: 8) The vector field Vp[x, y] = F =- has a potential function p[x, y] = a) (x² + y²)³2 b) d) Vx? +y?…

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Q: Match the vector field to its graph. 1. 2. = %3D 3. F (x, y) 1 = F (x, y) = F (x, y) 4. E 5.

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Q: - Given the vector fields Å = yz az – 3x a, +x²y a, B = 3 a, – 4xy a, +y² az Petermine a unit vector…

A: Given that: A→=yzax-3xay+x2yazB→=3ax-4xyay+y2az

Q: Question 7 a) Consider the vector field F(r, y, z) = (2ry, r² + 2z, z°y²). %3D Find curlF.

A: Since you have asked multiple questions in single request so we will be answering only first…

Q: Theorem 7.5.4. The curvature of a smooth space curve defined by the vector valued function R(t) is…

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Q: Sketch the vector field.  F(x, y) =〈y, 1〉

A: The vector field: F(x,y)=<y,1>

Q: A vector field is given as G = (1/(√x² + xy))(e¯²ax +xzay), find the unit vector which is normal to…

A: The given vector fields are: G=1x2+xye-zax+xzayP=3x2ax-4yay We have to find the unit vector which is…

Q: 1. Find the divergence and curl of the following vector fields a. F = (1/y²)j b. F=y³z³i+ 2xyz³j +…

A: We have to find the divergence and curl of the given vector fields.

Q: H.W. draw the vector fields 1. F(xy) = 2xi – yj 2. F(xy) = xi -3yj 3. F(xy) 2i – xj %3D %3D %3D

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Suppose a vector function F(x, y) = 3xi + 2xyj + y ln z k moves along a path C where x = t², y = t +…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 4) Determine whether the vector field hlxiy)= y?i+ 12xy-e4)T is conservative conservative, deter…

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Q: QUESTION 2 Suppose that y is a g-dimensional vector space and that T: V→V and s:V→V are linear…

A: We will find out the required solution.

Q: Show that F = (3, 1, 2) is conservative. Then prove more generally that any constant vector field F…

A: Given: F = (3, 1, 2) To show: F is conservative. Also to show any constant vector field F = (a, b,…

Q: reply as soon as posible.

A: To find out the conservative.

Q: Sketch the vector field: F(x, y) = (1, 2y) Carefully draw at least four vectors in each of the four…

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Q: Question 3 Consider the vector field v(x) = i+ i+ 6k. y j + 6k. Vx²+y Vx²+y² a) Calculate /v• dr,…

A: Given vectors is vx=xx2+y2i+yx2+y2j+6k To evaluate ∫Cv·dr where C is the line joining (8,0,8) to…

Q: How much work is required to move an object in the vector field F = 5 y² ỉ + 2xy] Along the curve C,…

A: Given: F=5y2i+2xyj  C1 is the line y=0 C2 is the line x=1 C3 is the line segment joining points 1,1…

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 山供 得 三 -5+ 5 X 三 -5+ ||| 三 5 BE 州 X x

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5

A: We can solve this using by draw a graph

Q: 3. Find the work of the vector field F(2, y, ) = yi along the curve which is obtained as the…

A: To find the work of the vector field Fx,y,z=yi along the curve obtained by the intersection of…

Q: 5. Let A E Mmn(F). Prove that v E F™ is in colspace(A) if and only if there exists some vector u e…

A: Here, we assume the matrix as linear transformation.

Q: Consider the vector field i = P(x, y) = –3y+ ¤(x² + y² – 1), ý = Q(x, y) = 3x +y(x² + y² – 1) | %3D

A: consider the following

Q: Compute the integral of ſA° · dľ°P2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector function…

A: We have to find the integral from point p1 TP p2.

Q: (20) Given the vector field i = (a² – y² + 2xz)î+ (xz – ry + yz)ĵ+(2² + x²)k. Find v x ở and show…

A: Given v→=x2-y2+2xzi^+xz-xy+yzj^+z2+x2k^

Q: ) Show that the vector field, F3 yz £ + zx ŷ + xy 2 c

A: Given: The vector field is, F3 = yz x^ + zx y^ + xy z^

Q: 2. Sketch the vector field F(x, y, z) = xi + yj + zk.

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Q: Match the vector field with its graph. F(x, y) = yi y 1信 5 5 y 5 -6+ -5+

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Q: (1) Give an example of a function z = f(x, y) and a unit vector i such that f(0,0) = 2, fy(0,0) = 1…

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Q: Determine the vector field of F. (x, y) = 12i – 4j 1

A: given isF(x,y)=12i-4jgraph of vector field of F is attached below

Q: 19. Consider the vector field V(x, y, z) = ( HÓ-DE) 1-y x²+(y–1)² » 2+(y-1)2 and the curves 8 : 2 +…

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 進 ↑ -6+ <||||||||||| Hex

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Q: 4. Given the vector field Č = p² sin o a, + (z² cos – 1)as + (p² – z)a, Determine the x-component of…

A: Given the vector field

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.