$3\mathrm{.}5$ An idealized velocity distribution is given by

$u=\frac{x}{1+t},v=\frac{y}{1+2t},w=0$

Calculate and plot

$($a$)$ the streamline; and $($b$)$ the pathline which pass through the point $(x_0,y_0,0)$ at time $t=0.$