Let a(t) = (– 5, 5, – 2)t + (2, 4, 6) and b(u) 3 (- 3,0, - 4)и + ( - 2, — 8, — 5). Find the acute angle (in degrees) between the lines:

Q: Let f(z) = x² +iy² where z and y are the real and imaginary parts, respectively of z and C is a…

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Q: Evaluate F.dr where F(x, y) = xry i+e*j and C is the line segment from (2, 0) to (4, 0). а) 0 b) 2…

A: Line integral

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A: As per our guidelines we are suppose to solve only three sub-parts of a question. Kindly re-post the…

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A: Given data÷

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A: Explained below

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Q: E valuate f win Tydy tyxdx olE Cethe line seqment f&Om (0,2) to

A: on solving this we get the

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Q: calculate r(t) and T(t), and evaluate T(1).  r(t) = (et, t2)

A: rt=et, t2 Differentiating with respect to t, we get r't=detdt,  dt2dt=et,  2t Now,…

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A: We have to find derivative

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A: a) 0 is correct.

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A: Given x=u2+v2,y=uv   u,v=2,-2

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A:

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r'"(t). 5,3K r(t) = t²i - 4tj + 3. %3D (a) r'(t) (b)…

A: Vector

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A: Given Fx,y,z=zi^+x2j^+yk^. We have to evaluate ∫CF⋅dr, where C is the line segment from 1,2,3 to…

Q: Evaluate F.dr where F(x, y) =xry i+e*j and C is the line segment from (2, 0) to (4, 0). a) 0 b) 2 c)…

A: use parametrization of a line segment and formula for the line integral.

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A: Given:        r(t)=⟨t,t2,t3⟩

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A: We have to find the values of a

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Q: dw dw Find ду and ду at the point (w, x, y, z) = (9,3,1,1) if w = x²y? + yz- z³ and x2+y² +z² = 11.

A: The solution of the problem is given in the next steps.

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A:

Q: F(x, y, z) = yzi + xzj + xyk (a) C₁: r₁(t) = ti + 3j+ tk, 0≤ t ≤9 (b) C₂: r₂(t) = t²i + tj + t²k, 0≤…

A:

Q: Calculate r' (t), T(t), and T(2) where r(1) = (3, r*). r' (t) = ( 6t ). ... ... ... 4t^3 ... T(t) =…

A:

Q: If u = x²zî + yz?j – xyk and 0 = x²yz then find the value of u. (To)

A: Consider a function fx,y,z. The gradient of the function can be defined as, ∇→f=∂f∂xi^+∂f∂yj^+∂f∂zk^…

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A: Given: z=x4+xy3x=uv4+w4y=u+vew The objective is to find ∂z∂u, when u=-3, v=2, w=0

Q: Calculate r'(t) and T(t), where r(t) = (2t – 5, 4 – 4t, 1 + 4t). %3D r'(t) = { %3D T(t) = {

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Q: Find R f(x, y) dA where f(x, y) = x and R = IR F(x, y) dA = [3, 9] x [4, 6].

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Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. v), y = (u + v) X = -

A: The formula for the Jacobian is: ∂(x,y)∂(u,v)=∂x∂u∂x∂v∂y∂u∂y∂v

Q: If r(t) = (t5, t, t²), find r'(t), T(1), r”(t), and r'(t) × r"(t). r'(t) = T(1) = r"(t) r'(t) x r(t)…

A: Given :rt=&lt;t6, t, t2&gt;

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A: Real part of f(z)

Q: Calculate r' (t), T(t), and T(3) where r' (t) = ( T(t) = ( T(3) = ( ). r(t) = (2t², 2t).

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Q: If F = (2x +y?)i + (3y –4x)j, evaluate F•dr around the triangle C of Figure 1, (a) in the indicated…

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Q: Evaluate F.dr where F(x, y) = xy i+ej and C is the line segment from (2, 0) to (4, 0). a) 0 b) 2 c)…

A: Consider the given information. Fx,y=xyi+exj and the line segment is from 2,0 to 4,0. Now, write the…

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A: Given f(x,y,z) =xy+z , x=s2 , y=st and z=t2. We need to calculate -df/ds.

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A: 1st derivative, 2nd derivative, dot product and cross product are evaluated.

Q: We are given w = 2yln(y+2z)+x2, where x=b√c, y=c-a2, and z=ab+1. Find the following ∂w/∂a at the…

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Q: Find r'(t), r"(t), r'(t) - r"(t), and r'(t) x r"(t). 1. r(t) = 2t'i – 4tj +°k (a) r(t) 4ti – 4j +…

A: Please refer the attached image for complete solution.

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Q: Find r'(t), r"(t), r'(t) · r"(t),

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Q: . Find the acute angle between the line joining A(1,2,3) and and the plane containing point…

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Q: Let f(z) = x² + iy where x and y are the real and imaginary parts, respectively of z and C is a…

A: ii