Instructions

Toy car $A$ is initially at $(9,-3),$ and is travelling at $\sqrt[\phantom{2}]{13}m{s}^{-1}$ in the direction $-2i+3j.$ Toy car $B$ is initially at $(-1,4),$ and travels at a constant velocity for $3$ seconds to $(5,7).$

a Write a vector equation for the position at time $t$ seconds for each toy car.

b Show that the paths of the cars intersect at $(3,6).$

c Will the cars collide? Explain your answer.