Chapter 6.4, Problem 2P

Let the position vector (with its tail at the origin) of a moving particle be $r=r(t)=$ $t^{2}i-2tj+\left(t^2+2t\right)k,$ where $t$ represents time.

(a) Show that the particle goes through the point $(4,-4,8).$ At what time does it do this?

(b) Find the velocity vector and the speed of the particle at time $t ;$ at the time when it passes though the point $(4,-4,8)$.

(c) Find the equations of the line tangent to the curve described by the particle and the plane normal to this curve, at the point $(4,-4,8)$.