Find the binormal vector, curvature and radius of curvature for the vector function r=3 cos 3ti + 3sin 3tj + 2tk

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A: since, y,-x,z3 and, ru,v=u cosv, u sinv,v So, F⇀ru,v=u cosv,-u sinv, v3 Now the normal upward vector…

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Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve 7(t)…

A: We will find out the required value.

Q: Consider the vector function given below. r(t) = (7t, 5 cos(t), 5 sin(t)) (a) Find the unit tangent…

A: Given:              r(t)=&lt; 7t , 5cost , 5sint &gt;⇒      r'(t) =&lt; 7, -5sin(t) , 5cos(t) &gt;⇒…

Q: (a) Find the unit vector of 2q where q=(8 sin 0,-8 cos 0,0).

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Q: Evaluate F.dS, where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 3, 0 < v < T…

A: Given that, F¯=y,-x,z5 and ru,v=u cos v, u sin v, v where 0≤u≤3 and 0≤v≤π. Find ru×rv as follows.…

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Q: Find the unit tangent vector T, the principal unit normal vector N, and the unit binormal vector B…

A: Consider the curve     Ct: rt =cost,sint,t (i) unit tangent vector                  The unit tangent…

Q: 2. Calculate the curvature, unit binormal vector and torsion for r(t) (e'cost)i+(e'sint)j +5k

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Q: d the curvature for the following vector function. r(t)=( cos(2t), -sin(2t), 4t )

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Q: Find the unit tangent vector at the indicated point of the vector function r(t) = est cos ti + et…

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Q: If r(t) = , then unit tangent is a principal unit normal is a and its curvature is a vector scalar

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Q: Consider the helix r(t) = (cos(1t), sin(1t), −1t). Compute, at t = 픔 A. The unit tangent vector T =…

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Q: Find the unit tangent vector T(t). r(t) = t²i + tj +4k, P(9, 3, 4) TO) (No Docpopcol

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Q: 7. For vectors a and b in R? prove Lagrange's identity: ||a x b|? = ||a|| ||b||? – (a · b)?

A: for vectors a and b in ℝ2 prove -lagrange's identity a×b2=a2b2-a·b2

Q: Consider the Vector function a.) Find the もこ0 arc leng th of rlt) from to b.) Find the curvature a…

A: The given vector function is rt=t,t2,23t3. a) Find the arc length of rt from t=0  to  t=1 as…

Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve = (3…

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Q: Compute the unit binormal vector and torsion of the curve r(t) = (8t, 5 cost, 5 sint (5, 8 sint, -8…

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Q: Find the unit tangent , nomaand binormaL vectors 2. 2-Ycet [csti * sint j + x].

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Find the unit tangent vector at the indicated point of the vector function r(t) = e3tk T(pi/2) = %3D…

A: Here the given vector is  r→(t)=e3t cos(t) i+e3t sin(t) j+e3t kr→(t)=e3t cos(t) , e3t sin(t)  , e3t…

Q: Find the principal unit normal vector for the helix r(t) = 2 cos ti + 2 sin tj + tk.

A: Given, r(t)=2 cost i+2 sint j+t k

Q: Find the curvature of the vector-valued function. r(t) = (e3t,e)

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Q: Hiwi fined the curvature for each the Fllbwing vector function Pt) =(44,-t, 2f>

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Q: #3. Use the cross product formula to calculate the curvature of the following vector function. r(t)…

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Q: ind a formula for a vector normal to the plane tangent to f(x,y) at (xo, Yo).

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Q: Consider the helix r(t)=(cos(2t),sin(2t),−4t)r(t)=(cos⁡(2t),sin⁡(2t),−4t). Compute, at t=π6t: A.…

A: Given r(t)=cos2t , sin 2t   , -4t      ; t=π6

Q: Evaluate /| F · dS , where F = and S is the helicoid with vector equation S r(u, v) 0<u < 1, 0 <…

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Q: Evaluate F. dS, where F = and S is the helicoid with vector equation r(u, v) = 0< u < 2, 0 < v <…

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Q: Calculate the curvature of the vector function when t= -7: 7(t) = (1+ 2t, 7 – 3t, -8 + 5t)

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