Consider the helix r(t) =<cos (5t),sin(5t),-1t>. Compute, at t=pi/6 :A. The unit tangent vector T=<-5/squareroot 101, -5 squareroot3/squareroot 101, -2/squareroot 101> B. The unit normal vector N=<squareroot 3/2, -1/2, 0>C. The unit binormal vector B=<___,___,___>

∫Czds, where C is the helix of radius 1 which rises counterclockwise from (1,0,0) to (-1,0,2π).

A charged particle enters a uniform magnetic field with a velocity vector at an angle of 45° with the magnetic field. The pitch of the helical path followed by the particle is p. The radius of the helix will be

For the given position vectors r(t) compute the unit tangent vector T(t) for the given value of t A) let r(t)=<cos2t,sin2t> Then T(pi/4) <__,__>B) let r(t)=<t^2,t^3> Then T(1)=<_,_>c) let r(t)= e^2t i+ e^-t j+ t K Then T(2)= _i+_j+_k

The range of the helix angle of the twist drill is ________Question 5Select one:a.> 0 and < 90b.0-180c.> 90 and < 180d.> 180e.90-180

Consider a particle travelling along the path given by c(t) = (−t, t, t^2). Here t denotes time. (a) Find the velocity and the speed of the particle.b) Find the unit tangent vector T(t), the principal normal vector N(t), the binormal vector B(t), the curvature κ(t) and the torsion τ (t) at time t.