Let C be the curve that consists of 4 straight intervals, beginning at (0, 0, 0) , going to (5, 2, 2), continuing to (8, 5, 6), then to (3, 3, 4), and finally returning to (0, 0, 0). Let F := (8x + 6y+3z+yz, 8x + 16y +3z + xz, 2x + 3y + 6z + xy). Use Stokes' theorem to compute the circulation of F around C: LF. dř =

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Q: ) Find the orthogonal trajectory of the family of curve given by y = In(r³ + b)

A: First formulate a differential equation to eliminate the parameter b . Then replace (dy/dx) by…

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Q: Consider the curve segments: 1 - to x = 4 and 3 1 to x = $1: y = x² from x S2: y = Vx from x = = 16.

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A: To evaluate ∫C F⇀·dr⇀ if F⇀x, y=4eyi⇀+4xeyj⇀ and the curve C is line segments from 0, 0 to 5, 4 to…

Q: Let C be the curve y = 2.5 In (6.25 – x²), for – 1.2 < x < 1.6. A graph of y follows. 4.6 4.5 4.4…

A: Here, y=2.5 ln6.25-x2. So,         y'=2.5ln6.25-x2'           =16.25-x26.25-x2'    =2.5·16.25-x2-2x…

Q: 13- Find the length of the curve a) r(t) = 4costi + 4sintj³ + 3tk³ 0< t < 3n b) r(t) = 4ti + 4tj¬ +…

A: Please refer the image,

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Q: Consider the piecewise smooth curve 0) to point B(4, 6, 1), shown in the following figure: 2=4-…

A: Given that A2,2,0 and B4,6,1 F= 2x-2z, 3y2,-2x Find the value of ∫CF·dr

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A: Note : The length L of a curve r(t)→=(x(t) , y(t)  ,z(t) )  from t=a  , t=b is given by…

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A: As per Bartleby guidelines I have authority to answer only one question. If you want other…

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A: Given rt=3t,4t−3,6t+1,  0≤t≤3Formula→Arc length=∫abr't dtr't=f't2+g't2+h't2    rt=xt,yt,zt

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Q: ) Draw a contour map of f(x,y)=x^2+4y^2 with an appropriate contour interval, showing at least six…

A: Solution of the problem as follows

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A: find derivative

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Q: (b) Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that F.…

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A: [Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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Q: Let C be the curve connecting (0,0,

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Q: 3. Evaluate (2ry - )+(r +2:)7+(2y- 2r2)k) - dr, where C is a simple curve from (-3,-2,-1) to (1, 2,…

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A: According to guidelines we solve only first question when the given questions are different.

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Q: 3. In Eercises, verify that the given point is on the curve and find the lines that are Haltangent…

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.