Consider the vector field given by F(x, y) = (6xy – 152*y)i + (3x² + 3y – 10a°y)j find a function f(x.y) such that F = Vf.Calculate | F.dr, where C is any length that connects the points A(1. –2) and B(0.3) in that order.

Q: Find the domain of the vector function r(t) = (t, √t — 4, √5 — t Domain: {t | <t< }

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Q: 6 1 Determine R(t) if ř'() = (201-4, and R(2) = (3, –5, 0).

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Q: H.W: Let V = {(x, y): x 20} with standard operation on R2. Is Va vector space?

A: A vector space is a set V that satisfies the following 8 conditions. Here two operations "+" and "."…

Q: Express the following vector function in a component form. r(t)=t°j+(cos 2t)k

A: The vector function is given as , rt=t3j^+cos2tk^ express in component form.

Q: Let A=[ Let B=A -t| 3. -2 where t is scalar, Fao which velve (s) of t is B singular?

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Q: Find the positive value for which the vector r(t) (2t, 9t?, 10t2 – 2) is perpendicular to r'(t). -

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Q: Find the positive value for which the vector r(t) = (3t, 10t², 7t² – 2) is perpendicular to r'(t).

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Q: COS 1,sin 2t) and R(0) = (1,0.–1). Let R be a vector function such that T(t) = (cos 2t, 2/2, Find An…

A: Given : T→=32cos2t , 12 , 32sin2t, R→0=1 , 0 , -1. To Find: The equation of the osculating plane,…

Q: Consider the following function. T: R² - R?, T(X, V) = (Vã, sxy, Vỹ) Find the following images for…

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Q: — ху )і — у X'

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Q: 33. Define T: R³ → R³ by y + 2z 2x +3y - z x +2y - 2z x - y a. Find all vectors in R' that are…

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Q: Consider the following position function in the plane: ř (t) = (t3 – 3t)i + 3t?j. %3D For this…

A: Position vector of any parametric curve r(t) can be given by a vector joining origin with that point…

Q: Consider the following function. T: R2 → R3, T(x, y) = (Vx, 4xy, vy) Find the following images for…

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Q: Find the unit tangent vector T(t) for r(t) = 2ti + 3tj + 6tk at t = −2. ○-4i-6j-12k ○_1 O 3 :- i- 49…

A: To find the unit tangent vector T(t), we first need to find the derivative of r(t): r(t) = 2ti + 3tj…

Q: Let R be a vector function such that T(t) Find The moving trihedral to the graph of R at t = 0. = co…

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Q: Find the point on the graph of z = - (2x² + y²) at which vector n = P = (-12, -10, -1) is normal to…

A: To find the point P on the graph of z=-2x2+y2 at which vector n=-12, -10, -1 is normal to the…

Q: -T - r(t) = (√√t² — 1, log (t² − 3t + 2),-

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Trigonometric function can be used as parameterization of many curves, here we use the following…

Q: Find curl(zi + xj+ yk).

A: Using definition of curl of vector.

Q: Consider the following vector functions: r(t)= tcost i + 2t sint j + 2 tk for t ≥ 0 t≥ 0. a. The…

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Q: Find the domain of the following vector-valued functions. i) Ř(t) = cos t î – k ii) Š(t) = (t², VE –…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the…

A: The objective is to find the vector function that represents the curve of intersection of the two…