For Exercises 5-6, find the velocity v(t) and acceleration a(t) of an object with the given position vector r(t). 6. r(t) = (3 cost, 2 sint, 1)

Q: Find the positive t when the vector r(t) = (4t, 4ť, 5t² – 6) is perpendicular to r' (t). -

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Q: Q3: A particle traveling in a straight line is located at the point (1,-1,2) and has speed 2 at time…

A: Solution :-

Q: Given an acceleration vector, initial velocity (uo.Vo). and initial position (xo.Yo). find the…

A: Given that: Acceleration, at=cost,5sint Initial position, x0,y0=3,0 Initial velocity, u0,v0=0,1 To…

Q: i If (a,ß), a<0 is the unit vector that is parallel to the tangent line to the curve y=-1x²-x at the…

A: The equation of the given curve is            y = -x2 - x        =&gt; dy/dx = -2x - 1 So, slope of…

Q: Find the positive t when the vector r(t) = (4t, 4t, 5t2 – 6) is perpendicular to r' (t). t =

A: We use the definition of the perpendicular of two vectors to find the positive value of t.

Q: Q2/ Find the velocity, speed, unit tangent vector and acceleration of the position vector f(t) at…

A: This is a problem related to vector and derivative of the function. Based on the general formula and…

Q: Here R^3 - {(0,0,0)}. please proof this using submersion. thank you.

A: Given: R3=(0,0,0) To find: The set M=(x,y,z)∈R3:x2+2y2+z2=4xyz a submanifold of R3.

Q: For the curve r(t), find the tangential (T) and normal (N) components of the acceleration vector.…

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Q: 3. An object moves with the trajectary which is the graph of the vector function R(t) = (t² +t)i +…

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Q: 40. A particle traveling in a straight line is located at the point (1,−1, 2) and has speed 2 at…

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Q: At time t 0, a particle is located at the point (1, 2, 3). It travels in a straight line to the…

A: To find the equation for the position vector r(t) of the particle at time t.

Q: 2. The position function of a particle is given by s(t) = (t – 1)²(t – 3) , where t is measured is…

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Q: Assume that an object moves on a trajectory according to the equations x(t)=t+cost, y(t)=t−sint.…

A: An object moves on a trajectory according to the equations  Differentiating  with respect to t, we…

Q: Calculate the directional derivative of f(x, y) = x²y in the direction of v = −3i+2j at the point P…

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Q: Q3. For the motion vector r(t) = ti+ In (cos t) j, find (i) The velocity (ii) The speed at t=T Write…

A: Given motion vector is, rt=t i^ +lncost j^ i To find velocity. vt=ddtrt=ddtt i^ +lncost j^=ddtt i^ +…

Q: Experiments show is that in temprature field, heat flows in the direction of maximum decrease of…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…