Two straight roads, indicated by vec$(r_1)(t)$ and vec$(r_2)(t),$ cross at an intersection.

$($a$)$ Model each road using vector equations, then determine the angle in degrees at which they cross $($round to two decimal places$).$

$($b$)$ Use the dot product to find the angle in degrees vec$(r_1)(t)$ makes with the positive $x-$axis $($round to two decimal places$).$

$($c$)$ Plot vec$(r_1)(t)$ on the graph above when $t=1.$