Question

Consider the path in R^3 given by
x(t) = cos t + t sin t
y(t) = sin t - t cos t
z(t) = cos t - t sin t
(a) Find the tangent vector to this path at t = pi.
(b) Is the tangent vector at t = pi perpendicular to the position vector at t = pi?
(c) Is the tangent vector to this path at t = 3pi parallel to the tangent vector at t = pi?

Answer 1

find x', y', z' at t=pi

Answer 2

of the dot of the position and tangent at t=pi is equal to 0, that property determines perpendicularity