Originally Posted by

**katie** Hi guys can anyone help me out with this?

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.

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

Mr F says:

x = 10 - t => t = 10 - x .... (1)

y = t^2 - 10t .... (2)

Substitute (1) into (2).

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

Mr F says: Substitute into the formula.

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

Mr F says: Use the dot product.

Thanks