A particle moves so that its position vector r at timet is r = a cos wt + bsin wt, where w is a constant and a and b are constant vectors. Show that (a) r i is independent of t, (b) the acceleration is everywhere towards the origin and proportional to T.

Q: 4. Let r(f) = ° 13 i - 6fj + Pk. (a) Find the unit tangent vector T(t) and T(3). | (b) Find the…

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Q: Let the position vector of a particle be given as r(t) = [et sint, et cost]. Find the tangential and…

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Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a sin 30 and =7t, where a is…

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Q: Find the acceleration at time t = 1 sec.

A: Given the position vector for a particle isr(t)=ti+t2j+t3kWe know that acceleration is the second…

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: If r(t) is the position vector of a particle in the plane at time t, find the indicated vector. Find…

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Q: a) The position of point moving in space is given by R(t) = 3 tan t i + cott j +2 lnt k, find the…

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Q: f(x, y, z) = sin(ry + z) foksiyonunun| P(1, 7/4, 7/2) noktasinda v = -2i + j+ 2k

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Q: The acceleration of a particle at any time >=0 is given by: dr a = == (25cos2t)i + (16sen2t)j +…

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Q: Find the directional derivative at (1, 1) if Vƒ(1, 1) = (3,−1) in the direction of the unit vector u…

A: Use the formula of directional derivative.

Q: The force exerted by an electric charge at the origin on a charged particle at the point (x,y,z)…

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Q: Find dr Ct) for the vector functions. dt r(t) = (1-2t)it Ct cos t)j -t %3D

A: To find dr(t)/dt

Q: An airplane took off from point (3, 0, 0) at an initial velocity, v(0)= 3j with an acceleration…

A: Let r(t) be a position vector of a particle at time t. Then the velocity vector  v(t)=ddtr(t) Also…

Q: 7(1) = 1°i – 4tj – gk

A: we have to calculate the acceleration vector of a particle if its position vector is given as…

Q: Q3) For the vector function f(t) = [2e", te?, 3 te? 1, Determine the point of %3D tangency and the…

A: We have to find the point of tangency and unit tangent vector at t=2.

Q: Let 7(t) = ti+tj+t?k be the position vector of a moving particle. Determine the velocity vector. (a)…

A: Option C is correct

Q: Find a unit vector in the direction in which f(x, y, z) = 3x³z² + 3y³z +24z - 3 increases most…

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Q: The position of point moving in space is given by R(t) = 3 tan t i+ cot t j + 2 lntk, find the…

A: We will find out the required velocity and acceleration vector functions.