Given the vector equation R(t) = (4 – 3t?)i + (t³ – 3t)j, find the angle between N(1) and R"(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: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: As per given by the question, there are given: a→t=6t, 5sint, cos6tv→0=4, 3, 5r→0=3, -4, -4 Now, For…

Q: Find the velocity and acceleration vectors in terms of u, and u. r= a(9 + sin t) and 0 = 3 - e ',…

A: we derivative to find velocity and acceleration

Q: Sketch the curve of the vector function r(t) = 3ti+ (3t + 1)j,-1<ts2, and indicate the orientation…

A: The given curve in vector form: r(t)=3ti+(3t+1)j The point of t is -1≤t≤2 To find the curve at the…

Q: Given the vector u = 2i + 6j, find the magnitude and angle in which the vector points (measured…

A: Given :u=-2i+6j

Q: Find the velocity and acceleration vectors in terms of u, and ue en r=6 sin t and 0= 9t

A: The velocity is given by            v = r' ur +rθ' uθandThe accerleration is given by        a =r"-r…

Q: cos(ti) + t^3j and the initial position R(0) = i − 2j.

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Q: Find the velocity vector for the position vector 7 (t) = (sin(7t), 6t°, e¯24).

A: Given,           The position vector is r→t=&lt;sin7t,6t9,e-2t&gt;.

Q: Find the value of x so that the vector i+2j+xk   makes and angle  pi/4  of  with the positive…

A: i+2j+xkTo Find: Value of x so that the vector makes an angle of π4 with the positive z axis.

Q: Q4/ For the force system shown in Fig. (1), find the forces F1 & F2 (Using Vectors) 30 45 F2 15

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Q: Find the velocity and acceleration vectors in terms of u, and ug- r= a(4+ sin t) and 0 =9- e -t,…

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Q: Given the vector u (5, – 2), find the magnitude and - angle in which the vector points (measured…

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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: Evaluate 1+ x° + y°dS, where S is the helicoid with vector equation т(и, и) — 0 <u < 3, 0 < v< T

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Q: Find the position vector R(t) given the velocity V(t) = 4e" i+ 4 cos(4t) j+ 12tk and the initial…

A: To find the position vector by the given velocity vector.

Q: The graph of the vector function r (t) = 2i + t²j+ tk is

A: Given function is r^t=2i^+t2j^+tk^. Plot the graph of the vector function. Choose some values for t…

Q: Find the vector equation for the line of intersection of the planes 32 + 2y :0 ánd 3* + ,0 ) +t(6, r…

A: To find the equation of line intersection of given planes.

Q: A point, p, is moving with acceleration 6t j - k at time t. If at t 1, the coordinates of P are (1,…

A: Answer

Q: D. Find the Iimit of the vector position r(t) = e "i+ j+ cos 2t k when t=0

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Q: Determine a direction derived from the point P and in the direction of the versor vector → informed…

A: Given:  Let f be a differentiable function at the point (a, b). Then f has a directional derivative…

Q: Find the velocity and acceleration vectors in terms of u, and ug. de = 5t, where a is a constant r=…

A: Introduction: The velocity of the function represents the function's rate of change with respect to…

Q: Find the velocity and acceleration vectors in terms of u, and ug- de = 5t, where a is a constant r=a…

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Q: Consider the given vector equation. r(t) = (4t – 2, t2 + 2) (a) Find r'(t).

A: Given ,rt=&lt;4t-2,t2+2&gt;

Q: the vectors y₁, y₂, Y3 (where y; E R² V i) must be linearly dependent?

A: Given the vectors y1, y2 and y3 in the vector space R3.

Q: Given the vector function 7(1)=(31²-1, 1-8√F³, 12t-4), find the speed & arc length of the curve on…

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Q: The graph of the vector function r(t) = ti +t²j+2k is

A: Graph of vector function  r(t) is :  r(t)= t i + t2 j + 2k

Q: A ball is thrown eastward into the air from the origin (in the direction of the positive x-axis).…

A: We have given The initial velocity v0 = 50i+ 80k and the acceleration vector a = −4j − 32k.

Q: Find the position vector R(t) given the velocity V(t) = 16e" i + 10 cos(5t) j+ 15t2 k and the…

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Q: Find the position vector R(t) and velocity V(t) given the acceleration A(t) = 50eti + 20 cos(2t) j+…

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Q: Find the vectors T and N and the binormal vector B = T x N, for the vector-valued function r(t) at…

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Q: Evaluate /1+ x² + y°dS, where S is the helicoid with vector equation S r(u, v) 0 < u < 3, 0 < v <…

A: Given integral ∬S1+x2+y2dS, where S is helicoid with vector equation r^u,v=ucosv,usinv,v We have to…

Q: Find the position vector R(t) given the velocity V(t) = e'i+ 16 cos(4t) j+ 16t k and the initial…

A: Givenvt=eti+16cos4tj+16t3k

Q: A curve has vector equation r(t) = (In(sin t), In(cost),V2 E 0<t< T/2 Find an equation of the…

A: Given curve, rt=lnsint, lncost, 2t Point: -ln22, -ln22, π22 Equation of a plane passing through the…

Q: Find the acceleration vector for the position vector r(t): = (sin(11t), 2t", e-10t).

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Q: Find the velocity and acceleration vectors in terms of u, and ug. r= a(6 + cos t) and 0= 5+ e where…

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Q: If the position vector of a particle P is r(r) (3cos t,5sin7,4 cos t) a) Show that the speed of the…

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Q: Given the vector u = - 6i – 3j, find the magnitude and angle in which the vector points (measured…

A: Here we will find the magnitude and direction of given vector,

Q: А. Find the domain of the vector position r(t) + t+2 (t + 2) j + In(9 – t²) k

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Q: Given the vector function 7 (t) = (3t, 5t", – 3t° + 2) - Find the velocity and acceleration vectors…

A: Given that vector function r→ t=3t,5t2,-3t5+2 To find the velocity and acceleration at t=-1Solution…

Q: and ue. Find the velocity and acceleration vectors in terms of u, r= 5 sint and 0 = 8t

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Q: Given the vector function 7 (t) = (- 4t, – 5t°, 2t + 2) Find the velocity and acceleration vectors…

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Q: Given a the vector equation r(t) (4 + 4t)i + (1 + 1t)j + (1 + 4t)k, rewrite this in terms of the…

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Q: Given the vector function r(t) = (2t, t",- 3t +4) Find the velocity and acceleration vectors at t=…

A: Given, r→(t)=2t, t5, -3t4+4

Q: Find the velocity, acceleration, and speed of an object with position vector r(t) = (Vi, 4 + Vi,…

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Q: Find T(t) ,Ñ(t),B(t), and k(t) for the vector position r(t) = (e2t cos t) i + (e2t sin t)j+ 2k when…

A: We have given r→(t)=e2tcosti+e2tsintj+2k. To find the unit tangent vector T→(t) at t=0, first…

Q: The position vector in the xy plane is [t2,sin(t)].  What is the distance traveled by the particle…

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Q: Find the vectors T and N at the given point: r(t) = (cos t, sint, In sin t); (0, 1, 0).

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Q: The velocity of a particle is given in terms of the time t by v = sinti - 2cos(2t)j + t2k   where…

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Q: Find the positive t when the vector r(t) = (7t, 6t², 9t2 3) is perpendicular to r'(t). - t =

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