Compute : fr (Re z – 3z) dz where r is a directed line segment from z = 0 to z = i .

Q: Calculate fo(7x + 6y) i + (4x + 7y) j) dr where C is the circular path with center (a, b) and radius…

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Q: Compute the line integral (Баллов: 2) Jo ds, Cis the right half of circle x2 + y 16 (counter…

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Q: Given: ZWZX ZYZX; ZW = ZY Prove: ZX is a perpendicular bisector of WY

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Q: Calculate fol(3z + 4y) ỉ + (5x + 2y) ) · dř where C is the circular path with center (a, b) and…

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Q: 2 Consider the line L: y -1 +t|0, te R, and the plane T : x – 4y – z = 6. (a) Show that L is…

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Q: 3. a) Compute : S, (Re z – 3z) dz where r is a directed line segment from z = 0 to z= i . b) Let C…

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Q: (b) Let the distance between two adjacent planes parallel to the plane (hkf) in the direct lattice…

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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: Evaluate ſſ, Vy² – x² dA where boundary of R is the parallelogram bounded by the four lines

A: In this question, we evaluate the double integral by using the change of variable. The region is…

Q: he area bounded by the curve y = 3Vz and the lines z = 5 and z = 9 above the r – aris is_ quare…

A: Find the area of bounded curve with line x=5 and x= 9 above x-axis

Q: Use Green's Theorem to evaluate (V1+r) dr+2ry dy, where C is the triangle with vertices (0, 0),…

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Q: Let D be the half-disc in the xy-plane given by x +y <9. Calculate e-(x2+v)dA

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Q: Let θ be the angle between the line y = mx +b and the x-axis. Prove that         m = tan θ.

A: The slope of a line is the rate of change of the y-axis with respect to x. Formula for slope=riserun…

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: 2. Given: WX = YZ; ZWXZ = ZYZX Prove: WXYZ is a parallelogram

A: Parallelogram

Q: If C is the line segment from (1, 3) to, (0, 0), find the value of the line integral: 3y i+ 3x j) ·…

A: Given If C is the line segment from (1, 3) to, (0, 0),

Q: Evaluate the line integral So 7y dr + 3x dy where C is the straight line path from (2, la 7uda + 3z…

A: Introduction: A line integral is an integral that determines the function to be integrated along a…

Q: WX || ZY and Zs Z and Y are supplementary WXYZ is a parallelogram Given: Prove: W Y

A: It is given that,  WX ¯|| ZY¯  and ∠Z and ∠Y are supplementary To prove :- WXYZ is a parallelogram

Q: Calculate f((5x + 2y)i + (4x + 7y) 3) · dr where C' is the circular path with center (a, b) and…

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Q: 28. Given: WX ZY and Zs Z and Y are supplementary WXYZ is a parallelogram Prove: ZRYS RVST

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Q: What is the projection of r(t) = ti + t4j + etk onto the xz-plane?

A: Given: r(t)= ti+t4j+etk

Q: 22. Compute the contour integral (Баллов: 2) Sof (2) dz, z E C, if f (z) = and path is semicircle z…

A: Topic:- application of integration

Q: 7 Prove : id Is perpendicular line to ra duic at its outer end point ,then t ang ent to the cirde is

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Q: 3) Consider the line L in R? spanned byp = (6). Let PL(u) be the orthogonal %3D projection of the u…

A: b = 4

Q: Given: BR and DM Z1E2 23E24 Prove: ABCD is a parallelogram 1 M A

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Q: Find the projection in the ry plane of the curve of intersection of the surfaces 222 = r² + y? and r…

A: Find your answer below

Q: Calculate Se(5x + 3y) i + (4x + 3y) j) · dĩ where C is the circular path with center (a, b) and…

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Q: 4. Evaluate the line integral / r y* ds where C is the right half of the circle r² + y² = 16.

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Q: Use Stoke 's Theorem to evaluate [ . dr, where v = y²i + xyj + xzk, and c is the bounding curve of…

A: We have to solve the given problem by using stokes theorem.

Q: Evaluate 36e dz, where C'is the polygonal path Oto consisting of the line segments from z = 0to z =…

A: The given integral is                                       ∫C36ezdz,  where C is the polynomial…

Q: Consider in the following figure: CB = 4CN, NA =5NX and M the midpoint of the AB side. Let CN=u and…

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Q: Find the distance from a point P(x1, y1, Z1) to the plane Ax + By + Cz = D.

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Q: Use the Green's theorem to calulate So (3x²y – xy? – 3.x²y²) dx + (x³ – 2.x³y+ x²y) dy, where C is…

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Q: Let f(z) = 5z + 14, and let C1 be the line segment from z = 0 to z = 2, let C2 be the line segment…

A: In this question, we calculate the complex integral along the given contour joining vertices of the…

Q: Use Stoke 's Theorem to evaluate [ V. dr, where v= y²i + xyj + xzk, and c is the bounding curve of…

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Q: Prove that (x+) ) is the rolution on the dipporen tial equation y'+ y-e 9= C,e*+ C2x + Cg, y" - 4 y"…

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Q: Let P denote the path r(t) = (7cost), where 0<t< 2n, and compute ſpF - dĩ where F = (!+ty 4 sin…

A: Let F→x,y be a vector field and r→t=xt,yt be the path of an object, where t1≤t≤t2. The line integral…

Q: 2. Evaluate the given line integral, (-y, x – y) · dR, where C is the line segment from (2,0) to (0,…

A: Using parametric equation, line integration is evaluated.

Q: can u help me with pullbacks and integration plz

A: Given that the integral,

Q: Let f(x, y, z) = eª + zy² and let C be a straight line segment connecting the points (4,2,1) and…

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Q: Calculate fc((7x + 6y) i + (4x + 7y) j) dr where C is the circular path with center (a, b) and…

A: The path is given as the circular with center (a, b). Now the integral is: I=∫C (7x+6y)i→ +…

Q: a) Evaluate /| (-ri-yj+2: k) · n dS, where o is the portion of the paraboloid z = 3x2 + 3y? between…

A: Define a function fx,y=z or fx,y=3x2+3y2.  So, the flux integral is:…

Q: Let F = -2yi + 2xj. Use the flux form of Green's Theorem to compute F·n ds where C is the positively…

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Q: Evaluate the line integral Levis where C is the half circle x² + y² = 1, y ≥ 0. x² + y² ds

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Q: If C is the line segment from (8, 1) to, (0,0), find the value of the line integral: Se(8y² i+x3) ·…

A: First we have to write the equation of the line segment C and then convert the given line integral…

Q: E is the midpoint of Ad of a parallelogram ABCD.F is any point of diagonal BD such that 4DF=BD.EF if…

A: Given: 4DF=BD Construction: Draw the diagonal AC. It will intersect the diagonal BD at point H.

Q: Show that a indeed perojective plane of gives 0rder BİBD (n+n+,n+),!

A: We need to prove that a projective plane of order n indeed gives a BIBD (n2+n+1, n+1, 1)

Q: Given: APQR has a right 2Q. M is the midpoint of PR. Prove: MP = MQ = MR

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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.