Q3. The acceleration of a particle moving in space is a(t) = (-3cost)i + (-3sint)j at t = 0 the particle passed through the point (3,0,0) with velocity v(0) = 3j + 2k. Find: 1. ř(t) 2. The unit tangent vector at t = t 3. Find the arc length of the particle for 0 < t < n

Q: #2. Consider the following vector function. r(t) = (t,3t²,-t²). (a) Find the arc length function.…

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Q: dy dz - 182 + 72"y + y² = - 10 Given the equation below, find 36 1822(3 – 14z3y) 7z%6 + 2y dy dr…

A: Given,            -18x3+7x36y+y2=-10

Q: *r(t) = (cos(3t), 1-sin(3t), 3 sin(3t) + cos(3t)) 8. For the space curve r, compute values at t =…

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Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

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Q: Let r(t) = (-3t³-4, -3e¹, 5 sin( - 3t)) Find the unit tangent vector T' (t) at the point t = 0 T(0)…

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Q: Aunit tangent vector to the curve r03[sin(t), 31, cos(f)] at the point A (0, 3Tt, 1) is given by 3.…

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Q: The acceleration of a particle moving in space is ã(t) = (-3cost)i +(-3sint)j at t = 0 the particle…

A: Here, a⇀(t)=(-3cost)i+(-3sint)j is the acceleration of a particle. (1) Now,  v⇀(t)=∫a(t)⇀dt+C…

Q: For the curve r(t), write the acceleration in the form a+T+aNN. r(t) = (6t sin t+ 6 cos t)i + (6t…

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Q: Find the unit tangent vector to the curve defined by =(- 4t, 4t, V49 - t) at t = - 6. T(- 6)

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Q: f(x) = (-x² + x)ln(x³ + 2x) f'(x) = ? %3D

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Q: Q3. For the motion vector r(t) = e cost i + e'sint j find: (i) (ii) aT

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Q: 8. Given the vector r(t) = (sint,cos?, In(cos?)), find the equation of the tangent line in…

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Q: 1. Find the unit tangent vector to r(t) = at t = n.

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