Q1) consider the curve C given by:

C : r(t) = (sin t t cos t)i + (cos t + t sin t)j + square root of 3 /2 t²k, t [ /4; 2 ].

(a) Find the equation of the tangent line to the curve when t = /2

(b) Find the unit tangent vector, T(t), for this curve for any t.

(c) Compute the normal vector to C at every t; 0 t 2.

(d) Compute d/dt (r(t) , (r'(t) x r''(t))) at t =

(e) Find the arc length of C.