20. Evaluate J Vx + 2y ds, where C is a. the straight-line segment x = t, y = 4t, from (0, 0) to (1, 4). b. C U C;; C, is the line segment from (0, 0) to (1, 0) and C, is the line segment from (1, 0) to (1, 2).

Q: Evaluate the line integral. | (9x – 9y) ds C C : x² + y² = 64 | (9x – 9y) ds = C

A: Explanation of the solution is given below...

Q: We know that S(x,y)dx + g(x,y)dy] = Se f(x,y)dx +Seg(x,y)dy. Use this knowledge to evaluate S.y dx+x…

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Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x=1+2t, y=5+15t, z=-2+6t, then…

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Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x = 1+2t, y=5+15t, z=-2+6t,…

A: given : the equations of two skew lines are: L1: x=1+t, y=1+6t, z=2tL2: x=1+2t, y=5+15t, z=-2+6t D…

Q: 20. Evaluate l Vx + 2y ds, where C is a. the straight-line segment x = t, y = 4t, from (0, 0) to (1,…

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Q: 2. Let j = Find the point on the line y x that is closest to j. %3D %3D 26

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Q: If D is the distance between the skew lines L1 x=1+1, y=1+61, z=21 L2 x=1+2t, y=5+151, z= -2+61.…

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Q: Evaluate the line integral ∫_c (2x − y) dx − (x+ 3y) dy , where C is a straight line from (1,1) to…

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Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: 4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as…

A: See the attachment

Q: dw dw Find ду at the point (w, x, y, z) = (- 4,1, - 1,1) if w = 4x y + 4yz - 4z° and x? + y? + z² =…

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Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

Q: 4. ( , Give a case in which |(x, y) x||yll. 5. Let X e PQ. Show that if X (1-t)P+Q, where t> 1, then…

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Q: 2人+人 2X PM the From Pi (x,,y,z,) to Pz (xz, Yz, Zz Prove that the Midpoint of the line Ssegment 12…

A: Let the 2 points in the line segment be,

Q: 2. Let c be the line from 5 to 2 + 3i. Find i. S. zdz ii. S. ždz

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Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x=1+2t, y=5+15t, z=-2+6t, then…

A: here we the formulae   the a plane have normal n→=<a,b,c> and passes through a point (x1 ,y1…

Q: (a) Compute S ædx + ydy + (x + y – 1)dz where C'is the line segment from (1, 1, 1) to (2, 3, 4).

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Q: Compute the length of the curve over the given interval. r(t) =〈3t, 4t − 3, 6t + 1〉, 0 ≤ t ≤ 3

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

Q: 3. For the lines L;:x = 4t – 1, y=t- 3, z=1 and L2: x= 12t + 11, y=1+ 6t, z= 2 + 3t a. Show that the…

A: Answer

Q: Find a parameterization, x = x(1), y = y(t), tE [0, 1], for the line segment from (2, -1) to (5, 5).

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Q: Compute (z + y²)dS where C' is the line segment from (3, 4, 0) to (1, 4, 2). 1. 34/2 2.42 /2 3. 14/2…

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Q: Hwi Sind the vecter Paralle I to the line metersell bet ween the flanes and X+y=2 2) X-2y+47-2 and…

A: Two non parallel planes meet at a line. The direction of this line is perpendicular to the normal of…

Q: Find Duf at P. 2, -k 3' 2 f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u = i+ 3 -

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Q: where Projuct of in tegra tion SÃr dR A-zi-xj-YK and =dxi +arj +dzK dR and %3D the seguent of the…

A: Use line integral

Q: 15. When a line L is tangent to the circle 2 + v = 100 at the point (a, 6), find the equation of…

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Q: Evaluate yz dx +y dy +a dz, where C is the line segment from (2,0, –1) to (4, 1, 2).

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Q: If D is the distance between the skew lines 4 x=1+t, y=1+6t, z=2t L2 x=1+2t, y=5+15t, z=-2+6t, then…

A: first we will  convert given parametric equations of lines, then we will find  a1,b1,a2,b2 after…

Q: If D is the distance between the skew lines L: x=1+t, y=1+6t, z 2t L2: x=1+2t, y=5+15t, z= -2+6t,…

A: Two lines in space can be skew, parallel and intersecting. Lines are skew if they are neither…

Q: Find b∈R so that ∫C4x^2dy − 2xydx = 53, where C is the segment from (1, −5) to (−2, −3), followed…

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Q: 1. Evaluate 4x³ds, where C ie the line segment trom -2,-1,QL,4). らt Xz xlt)= (1-t)(-2) + t(1) E) :…

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

Q: Evaluate S(-x+y+z)dx + (x+y-z)dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to (3,-2,…

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Q: Let C be the line segment connecting 0 to ni. Then f. 1-e2z dz =

A: we have to find integration

Q: Let y = [3] and u = [2] to the line through u and the origin. Compute the distance from y

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Q: (i) Evaluate S(z + 5i) dz where the path is the line From z = 1 to z = 2 +i

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Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

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Q: 3. Given the two following left rights: x = 3 +t D: y = -2 + 2t, where t eR z = -1+ 5t D2: (x,y,z) =…

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Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

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Q: Find Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

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Q: Which of the following lines pass through the point (7, 5) and is perpendicular to the line X + 3y =…

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Q: | 6. Let y = 3 and u = . Compute the distance from y to the line through u 1 2 and the origin.

A: Given: y=-231  and u=1-12 To compute: the distance from y to the line through u and the origin.…

Q: Evaluate | (x + iy' ) dz, where C is the straight line from z =1 to z=i.

A: given, C is the straight line from z=1 to z=i claim- evaluate the integral ∫Cx2+iy3 dz

Q: Let s(xy) = x²+y²_2x – 16y +10 =0 a cirdle be L (xy) = X-5y + 10=0 be a line.

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Q: Find the distance between two skew lines x = 5+t, y = 5 + 3t, z = 4 -t and x = 2t, y =t, z=t O 1 3 '…

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Q: .11 Compute (1/ry, 1/(x + y)) · dr along the curve (2t, 5t), 1 < t < 4.

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Q: If u=2x+y and v=x-2y then the st ream line is y2 x2 2ху+ 2 صواب ihi

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let f(x, y) = 4x + 3y and let 7 (t) be the line segment from (1, 1) to (–2, 5). Then 7 (t) =…

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Q: If p is the distance between the skew lines 4,:x=1+t, y=1+6t, z=2t Lz.x =1+2f, y=5+15f, z=-2+6t,…

A: Shortest distance between two skew lines

Q: 5. Find a and b so that the lines r¡(t) = (1+t, –1+ at, 1+3t) and r(t) = (3 – 3t, 2 – 4t, 1+ bt) :…

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Q: P to the line L is equal P that is orthogonal to t

A: Given as, The distance is given as, d=AP→sinθ