Not sure if this is in the right forum

A moving particle at time t ∈ [0, 10] (seconds) has position vector in metres from the origin (0, 0, 0) given by the vector function r(t) = (10 − t)i + (t 2 − 10t)j + sin tk.

Describe the path of the particle, as seen from above (the positive k-direction), and also describe it in three dimensions.

Find the curvature of the path, at t = 2π ≈ 6.28 seconds.

Find the angle between the path (at start and end-points) and the k-direction.

And this one too, i think i have to optimise the square but i don't think i have done it right

A particle’s path, in two dimensions, is described by its position vector (in metres and time t ∈ [1, 2] seconds) relative to point (0, 0, 0) by r(t) = (2t + 1)i + (4 − t^2 )j.

Find the value of t∗ at which the particle has greatest distance from (0, 0, 0).

Show that at position r(t∗ ), the particles velocity is not perpendicular to r(t∗ ).

Thanks heaps if you can help i can't get the right answers