Find the unit tangent vector T and the principal unit normal vector N for the following parameterized curve. Verify that |T|=|N| = 1 and T-N=0. r(t) = (5 sin t,5 cos t, 12t) T = N = (10 ... Suppose the vector-valued function r(t) = (f(t).g(t),h(t)) is smooth on an interval containing the point to. The line tangent to r(t) at t= to is the line parallel to the tangent vector r' (to) that passes through (f(to).g (to).h (to)). For the following function, find the line tangent to the curve at t= to. T r(t) = (17+ cost,6+ sin 2t,t); to = 2 to + (17-1/6+21 121 1 The line tangent to the curve at t= to is 17-t.6+2t.