Consider the curve described $by$ the position vector function

vec$(r)(t)=,$ for $0t2.$

Let $Pbe$ the point $(1,1,1)on$ the curve. Determine the following:

$(i)$ The unit tangent vector $atP$

$(ii)$ The curvature $atP$

$(iii)$ The $tangential$ component $of$ acceleration when $t=1$

$(iv)$ The normal component $of$ acceleration when $t=1$

$(v)$ The unit normal vector $atP$