Consider the following lines. r(t) = (3t+ 3, 5t + 1,4t + 4), for - o

Q: Find a function r(t) that describes the line through P(3,4,5) that is orthogonal to the plane 2x-z=4

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Q: 4. For the linear canonical system x' = Jx, x € R², determine the nature of the origin as a fixed…

A: Given canonical system x'= Jx  Case-1:-  det >0 if both Eigen value positive:- The product of the…

Q: Let C C R? be the path from (3, –2) to (3, 2) along the graph of the curve x – 5x?y? – 7x2 = 0.…

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Q: Let P(x1, y1) and Q(x2, y2) be two points in the plane. Prove that the equation of the line through…

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Q: 1 - Findthe lenght of the Curve a) r(t)* = (3cost)i³ + (3sint)j* + 4tk¬ for 0 < t < 2n b) r(t)* =…

A: Use formula of length of curve

Q: S. 1.110. Determine whether A dr is independent of the path C joining any two points if (a) A =…

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Q: Consider the path r(t) = (4t,2t 2 ,2lnt) defined for t > 0. Find the length of the curve between the…

A: Given the path r(t) = (4t, 2t2, 2ln t), t&gt;0. Find the length of the curve (4, 2, 0) and (20, 50,…

Q: Consider the two planes, T1: X = 4 – 2s + 3t - y = 1 +s + 2t z = 3 + 4s -t; s, t eR T2 : [x, y, z] =…

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Q: メ=1 45 the right of the line , y= what is the of the unbounded regron between the grea Curve Ond the…

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Q: 9) Find the time t when the line r(t) = ti + (1+ t)j + (1 + 3t)k intersects the plane x + 4y +6z =…

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Q: +3そ20 22 Prove that the line X21+2t ニー+3t is perpendicular to the plane X-2y+zz6

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: 8. (a) Show that the system i=y+xf(r)/r, j=-x+yf(r)/r (7=x²+y?) (*) has limit cycles corresponding…

A: Given part (a) x·=y+xfrry·=−x+yfrrr2=x2+y2 By transforming coordinates into polar coordinates Thus…

Q: [x = t - 1 Q.1 Verify that the lines L₁ y=1-t lz=1-t and find the distance between them. and [x = 2t…

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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: Let G = 3xy²a, + 2za, Given an initial point P(2, 1, 1) and a final point Q(4, 3, 1), find ſ G•dL…

A: Given G=3xy2ax+2zay and initial point P(2,1,1) and final point Q(4,3,1)

Q: (7) For each of the following pairs of lines, determine whether they are parallel (or are…

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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: Compute the length of the curve r(t)= (-3t, 3t + 7,–7t + 1) over the interval 0 <t <7

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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: 9x2 + 4y? at which the Find the point on the paraboloid z = normal line is parallel to the line…

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Q: 1. Find the equation of the plane containing the lines L1 and L2 given below: z = 4t + 3 z = -4s – 1…

A: Given :L1:  x=2t+1, y=3t+2, z=4t+3L2 : x=s+2, y=2s+4, z=-4s-1

Q: The line L(t) = (4 – 3t, 3, 1 +t) intersects the plane 3x – 3y + 2z = -16 at the point when t =

A: To find the point of intersection of the line and the plane, substitute the values of x,y, z from…

Q: Consider the curve 7(t) = (-5+ 2t, 5 + 5t) connecting the points (-5,5) and (-4, 7.5). Compute the…

A: consider the following

Q: Compute the length of the curve r(t)= (-5t, 4t – 3, – 5t + 5) over the interval 0 <t< 7

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Given the line integral | (2x2° + 6y) da + (6x – 2yz) dy + (3a² z² – y²) dz. Let C be the path that…

A: Note that the following integral reduces like this :

Q: Let L be the line whose symmetric equations are x-1=1=z+1. The equation of the plane through the…

A: Given: Symmetric equation of line L: (x-1) = (y-1)/9 = (z+1) Point P(2,3,-1)    To find: Equation of…

Q: Suppose that the three numbers r,, 12, and r3 are distinct. Show that the three functions exp (r,x),…

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Q: Find the symmetric equations of the L that is parallel to the two planes x + 2y - z= 2 and x + 6y+ z…

A: Given: Two planes, P1: x+2y-z=2, P2: x+6y+z=-3, Point P1, 2, 3

Q: 2. Let C be the closed path constructed by joining the segment [-2, 2] on the real axis with y(t) =…

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Q: Consider the path r(t) (14t, 7t, 7 In t) defined for t > 0. Find the length of the curve between the…

A: Given - r(t) = ( 14t, 7t2, 7lnt )  defined for t&gt;0 To find - The length of the curve between the…

Q: (b) Find the points on the line r(t) = (t, 1+2t, 1-2t) whose distance from the plane 2x - 2y+z=1 is…

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Q: Given the following two lines: D:: (x,y,z) = (2,0, 0) + k (0,3,0) and Dz: (x,y,2) = (2,0,2) +k…

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Q: Given two lines L1 : x =t+1, y = 3t + 1, z = 2t – 1, and L2 : x = 2t – 2, y = 2t + 3, z =t +1,…

A: The given lines are L1:x=t+1,y=3t+1,z=2t-1L2:x=2t-2, y=2t+3, z=t+1 and a plane H is parallel to both…

Q: -6 3 Let y = -5 and u = -4 -2 Compute the distance d from 3y to the line through u and the origin.

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Q: 1) which of the following pairs of planes cross along a straight line a) x+2y-3z-4=0…

A: General Equation of Plane: The general equation of the plane is given by where are constants Line:…

Q: The functions y1, Y2, · . . , Yn are linearly independent, if and only if W (y1, 22, *. Yn) (to) # 0…

A: Consider the following differential equation, y''+pxy'+qxy=0

Q: Find the plane determined L1: x=-1+t 12: x=1-4s by the intersecting lines: y=2+t y=1+2s 2=1-1-3-1-00…

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Q: Which of the following is an equation for the line through the point (2, 3) and perpendiçular to the…

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Q: Find the orthogonal trajectories of the family of lines 3x + 5y = C (A 3x - 5y = k (B 5x + Зу - k ©…

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Q: Draw the isoclines with their direction markers and sketch several solution curves, including the…

A: According to the given information, it is required to draw the isoclines with direction makers and…

Q: Which of the following is a parametrization of the line through P(-3, 2, –3) and Q(1, –1, 4) ? (a) x…

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Q: Q3: Let L;: x-2+33t, y 2t-1, z-4t and M: x+2y+z-11, and let (p) be thus point of intersection. Find…

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Q: Consider the intersection curve C in the first octant, between the surfaces s1: 2 = 1- r? S2 : 2 +…

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Q: Let Ti P(R)→ Pz CR) ope natag T(2+x)=D1 Expilain ke a liness Seech that T (1) = 0. and T(1+x²) = 2x.…

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Q: Suppose that T: R2→ R2 is linear, T(1, 0) = (1, 4), and T(1, 1) = (2, 5). What is T(2,3)? Is T…

A: Given,

Q: Consider the path r(t) = (4t, 2t², 2 In t) defined for t > 0. Find the length of the curve between…

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Q: At what point does the line r(t) = (6- 3t)i + (-2 + 2t)j + (-1- 3t)k intersect the yz-plane %3D O a.…

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